# How do you solve for x:  (x-3)(x-12)=(2x+5)(x-6)?

Jun 17, 2017

#### Answer:

$x = - 4 \pm \sqrt{82}$

#### Explanation:

First, use the FOIL method to expand both sides:

${x}^{2} - 12 x - 3 x + 36 = 2 {x}^{2} - 12 x + 5 x - 30$

${x}^{2} - 15 x + 36 = 2 {x}^{2} - 7 x - 30$

Now, move all the left terms to the right side by subtracting.

$0 = {x}^{2} + 8 x - 66$

Hmm... this can't be factored. But, we can complete the square to solve it. We know that ${\left(x + 4\right)}^{2} = {x}^{2} + 8 x + 16$, so:

$0 = {x}^{2} + 8 x + \textcolor{b l u e}{16} - \textcolor{b l u e}{16} - 66$

$0 = {\left(x + 4\right)}^{2} - 82$

Now, we can solve this using algebra:

$82 = {\left(x + 4\right)}^{2}$

$\pm \sqrt{82} = x + 4$

$- 4 \pm \sqrt{82} = x$

Final Answer