8(2x-4)=3x(2x-4)

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Solution for 8(2x-4)=3x(2x-4) equation: 


Simplifying
8(2x + -4) = 3x(2x + -4)

Reorder the terms:
8(-4 + 2x) = 3x(2x + -4)
(-4 * 8 + 2x * 8) = 3x(2x + -4)
(-32 + 16x) = 3x(2x + -4)

Reorder the terms:
-32 + 16x = 3x(-4 + 2x)
-32 + 16x = (-4 * 3x + 2x * 3x)
-32 + 16x = (-12x + 6x2)

Solving
-32 + 16x = -12x + 6x2

Solving for variable 'x'.

Combine like terms: 16x + 12x = 28x
-32 + 28x + -6x2 = -12x + 6x2 + 12x + -6x2

Reorder the terms:
-32 + 28x + -6x2 = -12x + 12x + 6x2 + -6x2

Combine like terms: -12x + 12x = 0
-32 + 28x + -6x2 = 0 + 6x2 + -6x2
-32 + 28x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-32 + 28x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-16 + 14x + -3x2) = 0

Factor a trinomial.
2((-8 + 3x)(2 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-8 + 3x)' equal to zero and attempt to solve:

Simplifying
-8 + 3x = 0

Solving
-8 + 3x = 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 + 3x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 3x = 0 + 8
3x = 0 + 8

Combine like terms: 0 + 8 = 8
3x = 8

Divide each side by '3'.
x = 2.666666667

Simplifying
x = 2.666666667

Subproblem 2
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
Solution
x = {2.666666667, 2}

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