3x(x-6)=(2x+2)(x-6)

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Solution for 3x(x-6)=(2x+2)(x-6) equation: 


Simplifying
3x(x + -6) = (2x + 2)(x + -6)

Reorder the terms:
3x(-6 + x) = (2x + 2)(x + -6)
(-6 * 3x + x * 3x) = (2x + 2)(x + -6)
(-18x + 3x2) = (2x + 2)(x + -6)

Reorder the terms:
-18x + 3x2 = (2 + 2x)(x + -6)

Reorder the terms:
-18x + 3x2 = (2 + 2x)(-6 + x)

Multiply (2 + 2x) * (-6 + x)
-18x + 3x2 = (2(-6 + x) + 2x * (-6 + x))
-18x + 3x2 = ((-6 * 2 + x * 2) + 2x * (-6 + x))
-18x + 3x2 = ((-12 + 2x) + 2x * (-6 + x))
-18x + 3x2 = (-12 + 2x + (-6 * 2x + x * 2x))
-18x + 3x2 = (-12 + 2x + (-12x + 2x2))

Combine like terms: 2x + -12x = -10x
-18x + 3x2 = (-12 + -10x + 2x2)

Solving
-18x + 3x2 = -12 + -10x + 2x2

Solving for variable 'x'.

Reorder the terms:
12 + -18x + 10x + 3x2 + -2x2 = -12 + -10x + 2x2 + 12 + 10x + -2x2

Combine like terms: -18x + 10x = -8x
12 + -8x + 3x2 + -2x2 = -12 + -10x + 2x2 + 12 + 10x + -2x2

Combine like terms: 3x2 + -2x2 = 1x2
12 + -8x + 1x2 = -12 + -10x + 2x2 + 12 + 10x + -2x2

Reorder the terms:
12 + -8x + 1x2 = -12 + 12 + -10x + 10x + 2x2 + -2x2

Combine like terms: -12 + 12 = 0
12 + -8x + 1x2 = 0 + -10x + 10x + 2x2 + -2x2
12 + -8x + 1x2 = -10x + 10x + 2x2 + -2x2

Combine like terms: -10x + 10x = 0
12 + -8x + 1x2 = 0 + 2x2 + -2x2
12 + -8x + 1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
12 + -8x + 1x2 = 0

Factor a trinomial.
(2 + -1x)(6 + -1x) = 0


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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2

Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {2, 6}

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