(x-12)(x+9)=(3-x)(x+13)

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Solution for (x-12)(x+9)=(3-x)(x+13) equation: 


Simplifying
(x + -12)(x + 9) = (3 + -1x)(x + 13)

Reorder the terms:
(-12 + x)(x + 9) = (3 + -1x)(x + 13)

Reorder the terms:
(-12 + x)(9 + x) = (3 + -1x)(x + 13)

Multiply (-12 + x) * (9 + x)
(-12(9 + x) + x(9 + x)) = (3 + -1x)(x + 13)
((9 * -12 + x * -12) + x(9 + x)) = (3 + -1x)(x + 13)
((-108 + -12x) + x(9 + x)) = (3 + -1x)(x + 13)
(-108 + -12x + (9 * x + x * x)) = (3 + -1x)(x + 13)
(-108 + -12x + (9x + x2)) = (3 + -1x)(x + 13)

Combine like terms: -12x + 9x = -3x
(-108 + -3x + x2) = (3 + -1x)(x + 13)

Reorder the terms:
-108 + -3x + x2 = (3 + -1x)(13 + x)

Multiply (3 + -1x) * (13 + x)
-108 + -3x + x2 = (3(13 + x) + -1x * (13 + x))
-108 + -3x + x2 = ((13 * 3 + x * 3) + -1x * (13 + x))
-108 + -3x + x2 = ((39 + 3x) + -1x * (13 + x))
-108 + -3x + x2 = (39 + 3x + (13 * -1x + x * -1x))
-108 + -3x + x2 = (39 + 3x + (-13x + -1x2))

Combine like terms: 3x + -13x = -10x
-108 + -3x + x2 = (39 + -10x + -1x2)

Solving
-108 + -3x + x2 = 39 + -10x + -1x2

Solving for variable 'x'.

Reorder the terms:
-108 + -39 + -3x + 10x + x2 + x2 = 39 + -10x + -1x2 + -39 + 10x + x2

Combine like terms: -108 + -39 = -147
-147 + -3x + 10x + x2 + x2 = 39 + -10x + -1x2 + -39 + 10x + x2

Combine like terms: -3x + 10x = 7x
-147 + 7x + x2 + x2 = 39 + -10x + -1x2 + -39 + 10x + x2

Combine like terms: x2 + x2 = 2x2
-147 + 7x + 2x2 = 39 + -10x + -1x2 + -39 + 10x + x2

Reorder the terms:
-147 + 7x + 2x2 = 39 + -39 + -10x + 10x + -1x2 + x2

Combine like terms: 39 + -39 = 0
-147 + 7x + 2x2 = 0 + -10x + 10x + -1x2 + x2
-147 + 7x + 2x2 = -10x + 10x + -1x2 + x2

Combine like terms: -10x + 10x = 0
-147 + 7x + 2x2 = 0 + -1x2 + x2
-147 + 7x + 2x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-147 + 7x + 2x2 = 0

Factor a trinomial.
(-21 + -2x)(7 + -1x) = 0


Subproblem 1
Set the factor '(-21 + -2x)' equal to zero and attempt to solve:

Simplifying
-21 + -2x = 0

Solving
-21 + -2x = 0

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

Add '21' to each side of the equation.
-21 + 21 + -2x = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -2x = 0 + 21
-2x = 0 + 21

Combine like terms: 0 + 21 = 21
-2x = 21

Divide each side by '-2'.
x = -10.5

Simplifying
x = -10.5

Subproblem 2
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
Solution
x = {-10.5, 7}

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