(2x-1)(2x+2)=10

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Solution for (2x-1)(2x+2)=10 equation: 


Simplifying
(2x + -1)(2x + 2) = 10

Reorder the terms:
(-1 + 2x)(2x + 2) = 10

Reorder the terms:
(-1 + 2x)(2 + 2x) = 10

Multiply (-1 + 2x) * (2 + 2x)
(-1(2 + 2x) + 2x * (2 + 2x)) = 10
((2 * -1 + 2x * -1) + 2x * (2 + 2x)) = 10
((-2 + -2x) + 2x * (2 + 2x)) = 10
(-2 + -2x + (2 * 2x + 2x * 2x)) = 10
(-2 + -2x + (4x + 4x2)) = 10

Combine like terms: -2x + 4x = 2x
(-2 + 2x + 4x2) = 10

Solving
-2 + 2x + 4x2 = 10

Solving for variable 'x'.

Reorder the terms:
-2 + -10 + 2x + 4x2 = 10 + -10

Combine like terms: -2 + -10 = -12
-12 + 2x + 4x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-12 + 2x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + x + 2x2) = 0

Factor a trinomial.
2((-2 + -1x)(3 + -2x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve:

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-2, 1.5}

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