# How do you solve (x + 7) ( 2x + 5) = - 7?

Jul 26, 2017

$x = - 6 , - \frac{7}{2}$

#### Explanation:

Solve:

$\left(x + 7\right) \left(2 x + 5\right) = - 7$

Expand the left side using the FOIL method.

$2 {x}^{2} + 19 x + 35 = - 7$

Add $7$ to both sides.

$2 {x}^{2} + 19 x + 35 + 7 = 0$

Simplify.

$2 {x}^{2} + 19 x + 42 = 0$

Factor the left-hand side.

$\left(x + 6\right) \left(2 x + 7\right) = 0$

Set each binomial equal to zero and solve.

$\left(x + 6\right) = 0$

$x = - 6$

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$\left(2 x + 7\right) = 0$

$2 x = - 7$

Divide both sides by $2$.

$x = - \frac{7}{2}$

Jul 26, 2017

$x = - \frac{7}{2} = - 3 \frac{1}{2}$ or $x = - 6$

#### Explanation:

$\left(x + 7\right) \left(2 x + 5\right) = - 7$

Expand the brackets.

$x \left(2 x + 5\right) + 7 \left(2 x + 5\right) = - 7$

$2 {x}^{2} + 5 x + 14 x + 35 = - 7$

$2 {x}^{2} + 19 x + 35 = - 7$

Add $7$ to both sides.

$2 {x}^{2} + 19 x + 35 + 7 = 7 - 7$

$2 {x}^{2} + 19 x + 42 = 0$

Factorise.

$2 {x}^{2} + 12 x + 7 x + 42 = 0$

$2 x \left(x + 6\right) + 7 \left(x + 6\right) = 0$

$\left(2 x + 7\right) \left(x + 6\right) = 0$

$2 x + 7 = 0$ and $x + 6 = 0$

$x = - \frac{7}{2}$ or $x = - 6$