(2x+1)(2x-3)=5

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Solution for (2x+1)(2x-3)=5 equation: 


Simplifying
(2x + 1)(2x + -3) = 5

Reorder the terms:
(1 + 2x)(2x + -3) = 5

Reorder the terms:
(1 + 2x)(-3 + 2x) = 5

Multiply (1 + 2x) * (-3 + 2x)
(1(-3 + 2x) + 2x * (-3 + 2x)) = 5
((-3 * 1 + 2x * 1) + 2x * (-3 + 2x)) = 5
((-3 + 2x) + 2x * (-3 + 2x)) = 5
(-3 + 2x + (-3 * 2x + 2x * 2x)) = 5
(-3 + 2x + (-6x + 4x2)) = 5

Combine like terms: 2x + -6x = -4x
(-3 + -4x + 4x2) = 5

Solving
-3 + -4x + 4x2 = 5

Solving for variable 'x'.

Reorder the terms:
-3 + -5 + -4x + 4x2 = 5 + -5

Combine like terms: -3 + -5 = -8
-8 + -4x + 4x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-8 + -4x + 4x2 = 0

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

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

Ignore the factor 4.

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 '(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
Solution
x = {-1, 2}

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