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

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


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

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

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

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

Combine like terms: 16x + -64x = -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((-1 + -2x)(2 + -1x)) = 0

Ignore the factor 16.

Subproblem 1
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

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 = {-0.5, 2}

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