(4x+8)(8x-4)=0

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Solution for (4x+8)(8x-4)=0 equation: 


Simplifying
(4x + 8)(8x + -4) = 0

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

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

Multiply (8 + 4x) * (-4 + 8x)
(8(-4 + 8x) + 4x * (-4 + 8x)) = 0
((-4 * 8 + 8x * 8) + 4x * (-4 + 8x)) = 0
((-32 + 64x) + 4x * (-4 + 8x)) = 0
(-32 + 64x + (-4 * 4x + 8x * 4x)) = 0
(-32 + 64x + (-16x + 32x2)) = 0

Combine like terms: 64x + -16x = 48x
(-32 + 48x + 32x2) = 0

Solving
-32 + 48x + 32x2 = 0

Solving for variable 'x'.

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

Factor a trinomial.
16((-2 + -1x)(1 + -2x)) = 0

Ignore the factor 16.

Subproblem 1
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

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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {-2, 0.5}

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