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

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


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

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

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

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

Combine like terms: -8x + 32x = 24x
(16 + 24x + -16x2) = 0

Solving
16 + 24x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8'.
8(2 + 3x + -2x2) = 0

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

Ignore the factor 8.

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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