2x(x+4)-4(x+4)=0

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Solution for 2x(x+4)-4(x+4)=0 equation: 


Simplifying
2x(x + 4) + -4(x + 4) = 0

Reorder the terms:
2x(4 + x) + -4(x + 4) = 0
(4 * 2x + x * 2x) + -4(x + 4) = 0
(8x + 2x2) + -4(x + 4) = 0

Reorder the terms:
8x + 2x2 + -4(4 + x) = 0
8x + 2x2 + (4 * -4 + x * -4) = 0
8x + 2x2 + (-16 + -4x) = 0

Reorder the terms:
-16 + 8x + -4x + 2x2 = 0

Combine like terms: 8x + -4x = 4x
-16 + 4x + 2x2 = 0

Solving
-16 + 4x + 2x2 = 0

Solving for variable 'x'.

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

Factor a trinomial.
2((-4 + -1x)(2 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4

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 = {-4, 2}

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