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

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


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

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

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

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

Combine like terms: -6x + 2x = -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 + -1x + x2) = 0

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

Ignore the factor 4.

Subproblem 1
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

Subproblem 2
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
Solution
x = {-3, 4}

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