(4x-8)(8x+2)=0

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Solution for (4x-8)(8x+2)=0 equation: 


Simplifying
(4x + -8)(8x + 2) = 0

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

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

Multiply (-8 + 4x) * (2 + 8x)
(-8(2 + 8x) + 4x * (2 + 8x)) = 0
((2 * -8 + 8x * -8) + 4x * (2 + 8x)) = 0
((-16 + -64x) + 4x * (2 + 8x)) = 0
(-16 + -64x + (2 * 4x + 8x * 4x)) = 0
(-16 + -64x + (8x + 32x2)) = 0

Combine like terms: -64x + 8x = -56x
(-16 + -56x + 32x2) = 0

Solving
-16 + -56x + 32x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-2 + -7x + 4x2) = 0

Factor a trinomial.
8((-1 + -4x)(2 + -1x)) = 0

Ignore the factor 8.

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

Simplifying
-1 + -4x = 0

Solving
-1 + -4x = 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 + -4x = 0 + 1

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

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

Divide each side by '-4'.
x = -0.25

Simplifying
x = -0.25

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 = {-0.25, 2}

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