(2x-1)(2x+1)=3x

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Solution for (2x-1)(2x+1)=3x equation: 


Simplifying
(2x + -1)(2x + 1) = 3x

Reorder the terms:
(-1 + 2x)(2x + 1) = 3x

Reorder the terms:
(-1 + 2x)(1 + 2x) = 3x

Multiply (-1 + 2x) * (1 + 2x)
(-1(1 + 2x) + 2x * (1 + 2x)) = 3x
((1 * -1 + 2x * -1) + 2x * (1 + 2x)) = 3x
((-1 + -2x) + 2x * (1 + 2x)) = 3x
(-1 + -2x + (1 * 2x + 2x * 2x)) = 3x
(-1 + -2x + (2x + 4x2)) = 3x

Combine like terms: -2x + 2x = 0
(-1 + 0 + 4x2) = 3x
(-1 + 4x2) = 3x

Solving
-1 + 4x2 = 3x

Solving for variable 'x'.

Reorder the terms:
-1 + -3x + 4x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-1 + -3x + 4x2 = 0

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


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 + -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 = {-0.25, 1}

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