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

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


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

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

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

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

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

Solving
0 = -2 + -2x + 4x2

Solving for variable 'x'.

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

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

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

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

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

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

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

Ignore the factor 2.

Subproblem 1
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

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 = {1, -0.5}

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