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

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


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

Remove parenthesis around (4x)
4x(4x) + -4x + -2 = 0

Remove parenthesis around (4x)
4x * 4x + -4x + -2 = 0

Reorder the terms for easier multiplication:
4 * 4x * x + -4x + -2 = 0

Multiply 4 * 4
16x * x + -4x + -2 = 0

Multiply x * x
16x2 + -4x + -2 = 0

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

Ignore the factor 2.

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 '(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 = {-0.25, 0.5}

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