(4x+2)*(4x-1)=0

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Solution for (4x+2)*(4x-1)=0 equation: 


Simplifying
(4x + 2)(4x + -1) = 0

Reorder the terms:
(2 + 4x)(4x + -1) = 0

Reorder the terms:
(2 + 4x)(-1 + 4x) = 0

Multiply (2 + 4x) * (-1 + 4x)
(2(-1 + 4x) + 4x * (-1 + 4x)) = 0
((-1 * 2 + 4x * 2) + 4x * (-1 + 4x)) = 0
((-2 + 8x) + 4x * (-1 + 4x)) = 0
(-2 + 8x + (-1 * 4x + 4x * 4x)) = 0
(-2 + 8x + (-4x + 16x2)) = 0

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

Solving
-2 + 4x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 2x + 8x2) = 0

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

Ignore the factor 2.

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 '(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
Solution
x = {-0.5, 0.25}

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