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

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


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

Reorder the terms:
4x(-2 + x) = -3(2x + -4)
(-2 * 4x + x * 4x) = -3(2x + -4)
(-8x + 4x2) = -3(2x + -4)

Reorder the terms:
-8x + 4x2 = -3(-4 + 2x)
-8x + 4x2 = (-4 * -3 + 2x * -3)
-8x + 4x2 = (12 + -6x)

Solving
-8x + 4x2 = 12 + -6x

Solving for variable 'x'.

Reorder the terms:
-12 + -8x + 6x + 4x2 = 12 + -6x + -12 + 6x

Combine like terms: -8x + 6x = -2x
-12 + -2x + 4x2 = 12 + -6x + -12 + 6x

Reorder the terms:
-12 + -2x + 4x2 = 12 + -12 + -6x + 6x

Combine like terms: 12 + -12 = 0
-12 + -2x + 4x2 = 0 + -6x + 6x
-12 + -2x + 4x2 = -6x + 6x

Combine like terms: -6x + 6x = 0
-12 + -2x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + -1x + 2x2) = 0

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

Ignore the factor 2.

Subproblem 1
Set the factor '(-3 + -2x)' equal to zero and attempt to solve:

Simplifying
-3 + -2x = 0

Solving
-3 + -2x = 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 + -2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2x = 0 + 3
-2x = 0 + 3

Combine like terms: 0 + 3 = 3
-2x = 3

Divide each side by '-2'.
x = -1.5

Simplifying
x = -1.5

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 = {-1.5, 2}

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