(x+12)(x-9)=-38

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Solution for (x+12)(x-9)=-38 equation: 


Simplifying
(x + 12)(x + -9) = -38

Reorder the terms:
(12 + x)(x + -9) = -38

Reorder the terms:
(12 + x)(-9 + x) = -38

Multiply (12 + x) * (-9 + x)
(12(-9 + x) + x(-9 + x)) = -38
((-9 * 12 + x * 12) + x(-9 + x)) = -38
((-108 + 12x) + x(-9 + x)) = -38
(-108 + 12x + (-9 * x + x * x)) = -38
(-108 + 12x + (-9x + x2)) = -38

Combine like terms: 12x + -9x = 3x
(-108 + 3x + x2) = -38

Solving
-108 + 3x + x2 = -38

Solving for variable 'x'.

Reorder the terms:
-108 + 38 + 3x + x2 = -38 + 38

Combine like terms: -108 + 38 = -70
-70 + 3x + x2 = -38 + 38

Combine like terms: -38 + 38 = 0
-70 + 3x + x2 = 0

Factor a trinomial.
(-10 + -1x)(7 + -1x) = 0


Subproblem 1
Set the factor '(-10 + -1x)' equal to zero and attempt to solve:

Simplifying
-10 + -1x = 0

Solving
-10 + -1x = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1x = 0 + 10
-1x = 0 + 10

Combine like terms: 0 + 10 = 10
-1x = 10

Divide each side by '-1'.
x = -10

Simplifying
x = -10

Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-10, 7}

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