6(x-6)-9(x-4)=(-3x+12)(x-6)

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Solution for 6(x-6)-9(x-4)=(-3x+12)(x-6) equation: 


Simplifying
6(x + -6) + -9(x + -4) = (-3x + 12)(x + -6)

Reorder the terms:
6(-6 + x) + -9(x + -4) = (-3x + 12)(x + -6)
(-6 * 6 + x * 6) + -9(x + -4) = (-3x + 12)(x + -6)
(-36 + 6x) + -9(x + -4) = (-3x + 12)(x + -6)

Reorder the terms:
-36 + 6x + -9(-4 + x) = (-3x + 12)(x + -6)
-36 + 6x + (-4 * -9 + x * -9) = (-3x + 12)(x + -6)
-36 + 6x + (36 + -9x) = (-3x + 12)(x + -6)

Reorder the terms:
-36 + 36 + 6x + -9x = (-3x + 12)(x + -6)

Combine like terms: -36 + 36 = 0
0 + 6x + -9x = (-3x + 12)(x + -6)
6x + -9x = (-3x + 12)(x + -6)

Combine like terms: 6x + -9x = -3x
-3x = (-3x + 12)(x + -6)

Reorder the terms:
-3x = (12 + -3x)(x + -6)

Reorder the terms:
-3x = (12 + -3x)(-6 + x)

Multiply (12 + -3x) * (-6 + x)
-3x = (12(-6 + x) + -3x * (-6 + x))
-3x = ((-6 * 12 + x * 12) + -3x * (-6 + x))
-3x = ((-72 + 12x) + -3x * (-6 + x))
-3x = (-72 + 12x + (-6 * -3x + x * -3x))
-3x = (-72 + 12x + (18x + -3x2))

Combine like terms: 12x + 18x = 30x
-3x = (-72 + 30x + -3x2)

Solving
-3x = -72 + 30x + -3x2

Solving for variable 'x'.

Reorder the terms:
72 + -3x + -30x + 3x2 = -72 + 30x + -3x2 + 72 + -30x + 3x2

Combine like terms: -3x + -30x = -33x
72 + -33x + 3x2 = -72 + 30x + -3x2 + 72 + -30x + 3x2

Reorder the terms:
72 + -33x + 3x2 = -72 + 72 + 30x + -30x + -3x2 + 3x2

Combine like terms: -72 + 72 = 0
72 + -33x + 3x2 = 0 + 30x + -30x + -3x2 + 3x2
72 + -33x + 3x2 = 30x + -30x + -3x2 + 3x2

Combine like terms: 30x + -30x = 0
72 + -33x + 3x2 = 0 + -3x2 + 3x2
72 + -33x + 3x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
72 + -33x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(24 + -11x + x2) = 0

Factor a trinomial.
3((3 + -1x)(8 + -1x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3

Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {3, 8}

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