(x-12)(x-4)=-7

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Solution for (x-12)(x-4)=-7 equation: 


Simplifying
(x + -12)(x + -4) = -7

Reorder the terms:
(-12 + x)(x + -4) = -7

Reorder the terms:
(-12 + x)(-4 + x) = -7

Multiply (-12 + x) * (-4 + x)
(-12(-4 + x) + x(-4 + x)) = -7
((-4 * -12 + x * -12) + x(-4 + x)) = -7
((48 + -12x) + x(-4 + x)) = -7
(48 + -12x + (-4 * x + x * x)) = -7
(48 + -12x + (-4x + x2)) = -7

Combine like terms: -12x + -4x = -16x
(48 + -16x + x2) = -7

Solving
48 + -16x + x2 = -7

Solving for variable 'x'.

Reorder the terms:
48 + 7 + -16x + x2 = -7 + 7

Combine like terms: 48 + 7 = 55
55 + -16x + x2 = -7 + 7

Combine like terms: -7 + 7 = 0
55 + -16x + x2 = 0

Factor a trinomial.
(5 + -1x)(11 + -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 '(11 + -1x)' equal to zero and attempt to solve:

Simplifying
11 + -1x = 0

Solving
11 + -1x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1x = 0 + -11
-1x = 0 + -11

Combine like terms: 0 + -11 = -11
-1x = -11

Divide each side by '-1'.
x = 11

Simplifying
x = 11
Solution
x = {5, 11}

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