(x-8)(x+9)=-2(x+31)

Solution for (x-8)(x+9)=-2(x+31) equation:

Simplifying
(x + -8)(x + 9) = -2(x + 31)

Reorder the terms:
(-8 + x)(x + 9) = -2(x + 31)

Reorder the terms:
(-8 + x)(9 + x) = -2(x + 31)

Multiply (-8 + x) * (9 + x)
(-8(9 + x) + x(9 + x)) = -2(x + 31)
((9 * -8 + x * -8) + x(9 + x)) = -2(x + 31)
((-72 + -8x) + x(9 + x)) = -2(x + 31)
(-72 + -8x + (9 * x + x * x)) = -2(x + 31)
(-72 + -8x + (9x + x2)) = -2(x + 31)

Combine like terms: -8x + 9x = 1x
(-72 + 1x + x2) = -2(x + 31)

Reorder the terms:
-72 + 1x + x2 = -2(31 + x)
-72 + 1x + x2 = (31 * -2 + x * -2)
-72 + 1x + x2 = (-62 + -2x)

Solving
-72 + 1x + x2 = -62 + -2x

Solving for variable 'x'.

Reorder the terms:
-72 + 62 + 1x + 2x + x2 = -62 + -2x + 62 + 2x

Combine like terms: -72 + 62 = -10
-10 + 1x + 2x + x2 = -62 + -2x + 62 + 2x

Combine like terms: 1x + 2x = 3x
-10 + 3x + x2 = -62 + -2x + 62 + 2x

Reorder the terms:
-10 + 3x + x2 = -62 + 62 + -2x + 2x

Combine like terms: -62 + 62 = 0
-10 + 3x + x2 = 0 + -2x + 2x
-10 + 3x + x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
-10 + 3x + x2 = 0

Factor a trinomial.
(-5 + -1x)(2 + -1x) = 0

Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '5' to each side of the equation.
-5 + 5 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5
Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-5, 2}