**Video Transcript**

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Transcript
**Factoring with Grouping**

Meet Vincent. He’s a painter and quite the eccentric. He just got a new commission, to embellish the façade of an old building on the fancy side of the town. The neighbors just want the ugly wall to disappear. For inspiration, he goes to take a look at the building. Those darn kids – they painted graffiti all over it. No matter, Vincent will paint over the mess. To help him cover the graffiti, Vincent can **solve quadratic equations** by **factoring and grouping**.

Back at home, as he considers the specifics of the building, he divises a strategy. What does he know? The front of the building is equal to an **area** of **45 yards squared**, but not to be included in the painting is the fire escape on the right side of the building, it's 2 yards **wide**, and the windows at the top of the building, they have a **height** of 3 yards. The painting must be in the shape of a **rectangle** with the height equal to **2 times the width**. Because he doesn’t know the width or the height, he uses the **variables**, **x** and **2x**.

### Setting up an equation

He sets up an equation and **sets** the total **area equal** to **45 yards squared**. The **quantity x plus 2 times the quantity 2x plus 3** is **equal to 45**. To calculate x, first we **FOIL**. Then, we **combine like terms**. Next, since this is a **quadratic equation**, to find the solution, we **modify** the **equation** - so it's **equal to 0**.

### Factoring by Grouping

Now we're ready to **factor with grouping**. First, find the **factors of ac that sum to b**. ac is equal to 2 times -39, so -78. b is 7. Now what factors of -78 sum to 7? Hmmm, let’s go through the list. Ahah, -6 and 13 will work. Now, we split up 7x into two terms, -6x and 13x. Pay close attention to this next step: use **parentheses** to group the 4 terms into 2 **binomials** and then **factor out** the **GCF** from **each binomial**. This can be tricky, so watch carefully. The end result is the **binomial**: x - 3 times the binomial 2x + 13, and the **product** is **equal to zero**. But not so fast, we have one last step.

Apply the **Zero Product Property** and **solve** for **both values** of 'x'. There one last thing to think about with this problem. You can’t have a **negative** length or width, so only **one** of the solutions is a **possible answer**. X is equal to 3 yards, so the height of the painting is equal to 6 yards and the width is equal to 3 yards.

Now that the math is done, Vincent can work on his masterpiece…