x(27-x)=(x-3)(32-x)

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Solution for x(27-x)=(x-3)(32-x) equation: 


Simplifying
x(27 + -1x) = (x + -3)(32 + -1x)
(27 * x + -1x * x) = (x + -3)(32 + -1x)
(27x + -1x2) = (x + -3)(32 + -1x)

Reorder the terms:
27x + -1x2 = (-3 + x)(32 + -1x)

Multiply (-3 + x) * (32 + -1x)
27x + -1x2 = (-3(32 + -1x) + x(32 + -1x))
27x + -1x2 = ((32 * -3 + -1x * -3) + x(32 + -1x))
27x + -1x2 = ((-96 + 3x) + x(32 + -1x))
27x + -1x2 = (-96 + 3x + (32 * x + -1x * x))
27x + -1x2 = (-96 + 3x + (32x + -1x2))

Combine like terms: 3x + 32x = 35x
27x + -1x2 = (-96 + 35x + -1x2)

Add 'x2' to each side of the equation.
27x + -1x2 + x2 = -96 + 35x + -1x2 + x2

Combine like terms: -1x2 + x2 = 0
27x + 0 = -96 + 35x + -1x2 + x2
27x = -96 + 35x + -1x2 + x2

Combine like terms: -1x2 + x2 = 0
27x = -96 + 35x + 0
27x = -96 + 35x

Solving
27x = -96 + 35x

Solving for variable 'x'.

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

Add '-35x' to each side of the equation.
27x + -35x = -96 + 35x + -35x

Combine like terms: 27x + -35x = -8x
-8x = -96 + 35x + -35x

Combine like terms: 35x + -35x = 0
-8x = -96 + 0
-8x = -96

Divide each side by '-8'.
x = 12

Simplifying
x = 12

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