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

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


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

Reorder the terms:
2x(-1 + 4x) = 4 + 2x
(-1 * 2x + 4x * 2x) = 4 + 2x
(-2x + 8x2) = 4 + 2x

Solving
-2x + 8x2 = 4 + 2x

Solving for variable 'x'.

Reorder the terms:
-4 + -2x + -2x + 8x2 = 4 + 2x + -4 + -2x

Combine like terms: -2x + -2x = -4x
-4 + -4x + 8x2 = 4 + 2x + -4 + -2x

Reorder the terms:
-4 + -4x + 8x2 = 4 + -4 + 2x + -2x

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

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

Factor out the Greatest Common Factor (GCF), '4'.
4(-1 + -1x + 2x2) = 0

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

Ignore the factor 4.

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 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

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

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

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

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {-0.5, 1}

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