(x-12)(x+8)-21=0

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Solution for (x-12)(x+8)-21=0 equation: 


Simplifying
(x + -12)(x + 8) + -21 = 0

Reorder the terms:
(-12 + x)(x + 8) + -21 = 0

Reorder the terms:
(-12 + x)(8 + x) + -21 = 0

Multiply (-12 + x) * (8 + x)
(-12(8 + x) + x(8 + x)) + -21 = 0
((8 * -12 + x * -12) + x(8 + x)) + -21 = 0
((-96 + -12x) + x(8 + x)) + -21 = 0
(-96 + -12x + (8 * x + x * x)) + -21 = 0
(-96 + -12x + (8x + x2)) + -21 = 0

Combine like terms: -12x + 8x = -4x
(-96 + -4x + x2) + -21 = 0

Reorder the terms:
-96 + -21 + -4x + x2 = 0

Combine like terms: -96 + -21 = -117
-117 + -4x + x2 = 0

Solving
-117 + -4x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-9 + -1x)(13 + -1x) = 0


Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9

Subproblem 2
Set the factor '(13 + -1x)' equal to zero and attempt to solve:

Simplifying
13 + -1x = 0

Solving
13 + -1x = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1x = 0 + -13
-1x = 0 + -13

Combine like terms: 0 + -13 = -13
-1x = -13

Divide each side by '-1'.
x = 13

Simplifying
x = 13
Solution
x = {-9, 13}

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