(x-12)(x+15)=0

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Solution for (x-12)(x+15)=0 equation: 


Simplifying
(x + -12)(x + 15) = 0

Reorder the terms:
(-12 + x)(x + 15) = 0

Reorder the terms:
(-12 + x)(15 + x) = 0

Multiply (-12 + x) * (15 + x)
(-12(15 + x) + x(15 + x)) = 0
((15 * -12 + x * -12) + x(15 + x)) = 0
((-180 + -12x) + x(15 + x)) = 0
(-180 + -12x + (15 * x + x * x)) = 0
(-180 + -12x + (15x + x2)) = 0

Combine like terms: -12x + 15x = 3x
(-180 + 3x + x2) = 0

Solving
-180 + 3x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-15 + -1x)(12 + -1x) = 0


Subproblem 1
Set the factor '(-15 + -1x)' equal to zero and attempt to solve:

Simplifying
-15 + -1x = 0

Solving
-15 + -1x = 0

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

Add '15' to each side of the equation.
-15 + 15 + -1x = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -1x = 0 + 15
-1x = 0 + 15

Combine like terms: 0 + 15 = 15
-1x = 15

Divide each side by '-1'.
x = -15

Simplifying
x = -15

Subproblem 2
Set the factor '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Solution
x = {-15, 12}

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