(2x-1)(2x+3)=45

Solution for (2x-1)(2x+3)=45 equation:

Simplifying
(2x + -1)(2x + 3) = 45

Reorder the terms:
(-1 + 2x)(2x + 3) = 45

Reorder the terms:
(-1 + 2x)(3 + 2x) = 45

Multiply (-1 + 2x) * (3 + 2x)
(-1(3 + 2x) + 2x * (3 + 2x)) = 45
((3 * -1 + 2x * -1) + 2x * (3 + 2x)) = 45
((-3 + -2x) + 2x * (3 + 2x)) = 45
(-3 + -2x + (3 * 2x + 2x * 2x)) = 45
(-3 + -2x + (6x + 4x2)) = 45

Combine like terms: -2x + 6x = 4x
(-3 + 4x + 4x2) = 45

Solving
-3 + 4x + 4x2 = 45

Solving for variable 'x'.

Reorder the terms:
-3 + -45 + 4x + 4x2 = 45 + -45

Combine like terms: -3 + -45 = -48
-48 + 4x + 4x2 = 45 + -45

Combine like terms: 45 + -45 = 0
-48 + 4x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-12 + x + x2) = 0

Factor a trinomial.
4((-4 + -1x)(3 + -1x)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

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

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

Divide each side by '-1'.
x = -4

Simplifying
x = -4
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

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

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

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-4, 3}