x(2x-4)=3(4x+6)

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Solution for x(2x-4)=3(4x+6) equation: 


Simplifying
x(2x + -4) = 3(4x + 6)

Reorder the terms:
x(-4 + 2x) = 3(4x + 6)
(-4 * x + 2x * x) = 3(4x + 6)
(-4x + 2x2) = 3(4x + 6)

Reorder the terms:
-4x + 2x2 = 3(6 + 4x)
-4x + 2x2 = (6 * 3 + 4x * 3)
-4x + 2x2 = (18 + 12x)

Solving
-4x + 2x2 = 18 + 12x

Solving for variable 'x'.

Reorder the terms:
-18 + -4x + -12x + 2x2 = 18 + 12x + -18 + -12x

Combine like terms: -4x + -12x = -16x
-18 + -16x + 2x2 = 18 + 12x + -18 + -12x

Reorder the terms:
-18 + -16x + 2x2 = 18 + -18 + 12x + -12x

Combine like terms: 18 + -18 = 0
-18 + -16x + 2x2 = 0 + 12x + -12x
-18 + -16x + 2x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
-18 + -16x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + -8x + x2) = 0

Factor a trinomial.
2((-1 + -1x)(9 + -1x)) = 0

Ignore the factor 2.

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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

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

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

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

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

Simplifying
x = -1

Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {-1, 9}

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