(2x-3)(2x+3)=15x-5

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Solution for (2x-3)(2x+3)=15x-5 equation: 


Simplifying
(2x + -3)(2x + 3) = 15x + -5

Reorder the terms:
(-3 + 2x)(2x + 3) = 15x + -5

Reorder the terms:
(-3 + 2x)(3 + 2x) = 15x + -5

Multiply (-3 + 2x) * (3 + 2x)
(-3(3 + 2x) + 2x * (3 + 2x)) = 15x + -5
((3 * -3 + 2x * -3) + 2x * (3 + 2x)) = 15x + -5
((-9 + -6x) + 2x * (3 + 2x)) = 15x + -5
(-9 + -6x + (3 * 2x + 2x * 2x)) = 15x + -5
(-9 + -6x + (6x + 4x2)) = 15x + -5

Combine like terms: -6x + 6x = 0
(-9 + 0 + 4x2) = 15x + -5
(-9 + 4x2) = 15x + -5

Reorder the terms:
-9 + 4x2 = -5 + 15x

Solving
-9 + 4x2 = -5 + 15x

Solving for variable 'x'.

Reorder the terms:
-9 + 5 + -15x + 4x2 = -5 + 15x + 5 + -15x

Combine like terms: -9 + 5 = -4
-4 + -15x + 4x2 = -5 + 15x + 5 + -15x

Reorder the terms:
-4 + -15x + 4x2 = -5 + 5 + 15x + -15x

Combine like terms: -5 + 5 = 0
-4 + -15x + 4x2 = 0 + 15x + -15x
-4 + -15x + 4x2 = 15x + -15x

Combine like terms: 15x + -15x = 0
-4 + -15x + 4x2 = 0

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


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

Simplifying
-1 + -4x = 0

Solving
-1 + -4x = 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 + -4x = 0 + 1

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

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

Divide each side by '-4'.
x = -0.25

Simplifying
x = -0.25

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 = {-0.25, 4}

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