(x-3)(x-12)=-20

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Solution for (x-3)(x-12)=-20 equation: 


Simplifying
(x + -3)(x + -12) = -20

Reorder the terms:
(-3 + x)(x + -12) = -20

Reorder the terms:
(-3 + x)(-12 + x) = -20

Multiply (-3 + x) * (-12 + x)
(-3(-12 + x) + x(-12 + x)) = -20
((-12 * -3 + x * -3) + x(-12 + x)) = -20
((36 + -3x) + x(-12 + x)) = -20
(36 + -3x + (-12 * x + x * x)) = -20
(36 + -3x + (-12x + x2)) = -20

Combine like terms: -3x + -12x = -15x
(36 + -15x + x2) = -20

Solving
36 + -15x + x2 = -20

Solving for variable 'x'.

Reorder the terms:
36 + 20 + -15x + x2 = -20 + 20

Combine like terms: 36 + 20 = 56
56 + -15x + x2 = -20 + 20

Combine like terms: -20 + 20 = 0
56 + -15x + x2 = 0

Factor a trinomial.
(7 + -1x)(8 + -1x) = 0


Subproblem 1
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

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 = {7, 8}

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