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

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


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

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

Reorder the terms:
-16 + 8x = -2x(3 + x)
-16 + 8x = (3 * -2x + x * -2x)
-16 + 8x = (-6x + -2x2)

Solving
-16 + 8x = -6x + -2x2

Solving for variable 'x'.

Combine like terms: 8x + 6x = 14x
-16 + 14x + 2x2 = -6x + -2x2 + 6x + 2x2

Reorder the terms:
-16 + 14x + 2x2 = -6x + 6x + -2x2 + 2x2

Combine like terms: -6x + 6x = 0
-16 + 14x + 2x2 = 0 + -2x2 + 2x2
-16 + 14x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
-16 + 14x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + 7x + x2) = 0

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

Ignore the factor 2.

Subproblem 1
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

Subproblem 2
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
Solution
x = {-8, 1}

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