(12-x)(15+x)=(8-x)(9+x)

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Solution for (12-x)(15+x)=(8-x)(9+x) equation: 


Simplifying
(12 + -1x)(15 + x) = (8 + -1x)(9 + x)

Multiply (12 + -1x) * (15 + x)
(12(15 + x) + -1x * (15 + x)) = (8 + -1x)(9 + x)
((15 * 12 + x * 12) + -1x * (15 + x)) = (8 + -1x)(9 + x)
((180 + 12x) + -1x * (15 + x)) = (8 + -1x)(9 + x)
(180 + 12x + (15 * -1x + x * -1x)) = (8 + -1x)(9 + x)
(180 + 12x + (-15x + -1x2)) = (8 + -1x)(9 + x)

Combine like terms: 12x + -15x = -3x
(180 + -3x + -1x2) = (8 + -1x)(9 + x)

Multiply (8 + -1x) * (9 + x)
180 + -3x + -1x2 = (8(9 + x) + -1x * (9 + x))
180 + -3x + -1x2 = ((9 * 8 + x * 8) + -1x * (9 + x))
180 + -3x + -1x2 = ((72 + 8x) + -1x * (9 + x))
180 + -3x + -1x2 = (72 + 8x + (9 * -1x + x * -1x))
180 + -3x + -1x2 = (72 + 8x + (-9x + -1x2))

Combine like terms: 8x + -9x = -1x
180 + -3x + -1x2 = (72 + -1x + -1x2)

Add 'x2' to each side of the equation.
180 + -3x + -1x2 + x2 = 72 + -1x + -1x2 + x2

Combine like terms: -1x2 + x2 = 0
180 + -3x + 0 = 72 + -1x + -1x2 + x2
180 + -3x = 72 + -1x + -1x2 + x2

Combine like terms: -1x2 + x2 = 0
180 + -3x = 72 + -1x + 0
180 + -3x = 72 + -1x

Solving
180 + -3x = 72 + -1x

Solving for variable 'x'.

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

Add 'x' to each side of the equation.
180 + -3x + x = 72 + -1x + x

Combine like terms: -3x + x = -2x
180 + -2x = 72 + -1x + x

Combine like terms: -1x + x = 0
180 + -2x = 72 + 0
180 + -2x = 72

Add '-180' to each side of the equation.
180 + -180 + -2x = 72 + -180

Combine like terms: 180 + -180 = 0
0 + -2x = 72 + -180
-2x = 72 + -180

Combine like terms: 72 + -180 = -108
-2x = -108

Divide each side by '-2'.
x = 54

Simplifying
x = 54

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