(x-2)(x+12)=15x

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Solution for (x-2)(x+12)=15x equation: 


Simplifying
(x + -2)(x + 12) = 15x

Reorder the terms:
(-2 + x)(x + 12) = 15x

Reorder the terms:
(-2 + x)(12 + x) = 15x

Multiply (-2 + x) * (12 + x)
(-2(12 + x) + x(12 + x)) = 15x
((12 * -2 + x * -2) + x(12 + x)) = 15x
((-24 + -2x) + x(12 + x)) = 15x
(-24 + -2x + (12 * x + x * x)) = 15x
(-24 + -2x + (12x + x2)) = 15x

Combine like terms: -2x + 12x = 10x
(-24 + 10x + x2) = 15x

Solving
-24 + 10x + x2 = 15x

Solving for variable 'x'.

Reorder the terms:
-24 + 10x + -15x + x2 = 15x + -15x

Combine like terms: 10x + -15x = -5x
-24 + -5x + x2 = 15x + -15x

Combine like terms: 15x + -15x = 0
-24 + -5x + x2 = 0

Factor a trinomial.
(-3 + -1x)(8 + -1x) = 0


Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-3, 8}

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