(5x-7)(3x+3)=12((x+1)(x+1))-3x(9-x)

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Solution for (5x-7)(3x+3)=12((x+1)(x+1))-3x(9-x) equation: 


Simplifying
(5x + -7)(3x + 3) = 12((x + 1)(x + 1)) + -3x(9 + -1x)

Reorder the terms:
(-7 + 5x)(3x + 3) = 12((x + 1)(x + 1)) + -3x(9 + -1x)

Reorder the terms:
(-7 + 5x)(3 + 3x) = 12((x + 1)(x + 1)) + -3x(9 + -1x)

Multiply (-7 + 5x) * (3 + 3x)
(-7(3 + 3x) + 5x * (3 + 3x)) = 12((x + 1)(x + 1)) + -3x(9 + -1x)
((3 * -7 + 3x * -7) + 5x * (3 + 3x)) = 12((x + 1)(x + 1)) + -3x(9 + -1x)
((-21 + -21x) + 5x * (3 + 3x)) = 12((x + 1)(x + 1)) + -3x(9 + -1x)
(-21 + -21x + (3 * 5x + 3x * 5x)) = 12((x + 1)(x + 1)) + -3x(9 + -1x)
(-21 + -21x + (15x + 15x2)) = 12((x + 1)(x + 1)) + -3x(9 + -1x)

Combine like terms: -21x + 15x = -6x
(-21 + -6x + 15x2) = 12((x + 1)(x + 1)) + -3x(9 + -1x)

Reorder the terms:
-21 + -6x + 15x2 = 12((1 + x)(x + 1)) + -3x(9 + -1x)

Reorder the terms:
-21 + -6x + 15x2 = 12((1 + x)(1 + x)) + -3x(9 + -1x)

Multiply (1 + x) * (1 + x)
-21 + -6x + 15x2 = 12((1(1 + x) + x(1 + x))) + -3x(9 + -1x)
-21 + -6x + 15x2 = 12(((1 * 1 + x * 1) + x(1 + x))) + -3x(9 + -1x)
-21 + -6x + 15x2 = 12(((1 + 1x) + x(1 + x))) + -3x(9 + -1x)
-21 + -6x + 15x2 = 12((1 + 1x + (1 * x + x * x))) + -3x(9 + -1x)
-21 + -6x + 15x2 = 12((1 + 1x + (1x + x2))) + -3x(9 + -1x)

Combine like terms: 1x + 1x = 2x
-21 + -6x + 15x2 = 12((1 + 2x + x2)) + -3x(9 + -1x)
-21 + -6x + 15x2 = (1 * 12 + 2x * 12 + x2 * 12) + -3x(9 + -1x)
-21 + -6x + 15x2 = (12 + 24x + 12x2) + -3x(9 + -1x)
-21 + -6x + 15x2 = 12 + 24x + 12x2 + (9 * -3x + -1x * -3x)
-21 + -6x + 15x2 = 12 + 24x + 12x2 + (-27x + 3x2)

Reorder the terms:
-21 + -6x + 15x2 = 12 + 24x + -27x + 12x2 + 3x2

Combine like terms: 24x + -27x = -3x
-21 + -6x + 15x2 = 12 + -3x + 12x2 + 3x2

Combine like terms: 12x2 + 3x2 = 15x2
-21 + -6x + 15x2 = 12 + -3x + 15x2

Add '-15x2' to each side of the equation.
-21 + -6x + 15x2 + -15x2 = 12 + -3x + 15x2 + -15x2

Combine like terms: 15x2 + -15x2 = 0
-21 + -6x + 0 = 12 + -3x + 15x2 + -15x2
-21 + -6x = 12 + -3x + 15x2 + -15x2

Combine like terms: 15x2 + -15x2 = 0
-21 + -6x = 12 + -3x + 0
-21 + -6x = 12 + -3x

Solving
-21 + -6x = 12 + -3x

Solving for variable 'x'.

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

Add '3x' to each side of the equation.
-21 + -6x + 3x = 12 + -3x + 3x

Combine like terms: -6x + 3x = -3x
-21 + -3x = 12 + -3x + 3x

Combine like terms: -3x + 3x = 0
-21 + -3x = 12 + 0
-21 + -3x = 12

Add '21' to each side of the equation.
-21 + 21 + -3x = 12 + 21

Combine like terms: -21 + 21 = 0
0 + -3x = 12 + 21
-3x = 12 + 21

Combine like terms: 12 + 21 = 33
-3x = 33

Divide each side by '-3'.
x = -11

Simplifying
x = -11

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