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

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

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

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

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

Multiply (-3 + 2x) * (3 + 2x)
(-3(3 + 2x) + 2x * (3 + 2x)) + -1x(x + -1) = 5
((3 * -3 + 2x * -3) + 2x * (3 + 2x)) + -1x(x + -1) = 5
((-9 + -6x) + 2x * (3 + 2x)) + -1x(x + -1) = 5
(-9 + -6x + (3 * 2x + 2x * 2x)) + -1x(x + -1) = 5
(-9 + -6x + (6x + 4x2)) + -1x(x + -1) = 5

Combine like terms: -6x + 6x = 0
(-9 + 0 + 4x2) + -1x(x + -1) = 5
(-9 + 4x2) + -1x(x + -1) = 5

Reorder the terms:
-9 + 4x2 + -1x(-1 + x) = 5
-9 + 4x2 + (-1 * -1x + x * -1x) = 5
-9 + 4x2 + (1x + -1x2) = 5

Reorder the terms:
-9 + 1x + 4x2 + -1x2 = 5

Combine like terms: 4x2 + -1x2 = 3x2
-9 + 1x + 3x2 = 5

Solving
-9 + 1x + 3x2 = 5

Solving for variable 'x'.

Reorder the terms:
-9 + -5 + 1x + 3x2 = 5 + -5

Combine like terms: -9 + -5 = -14
-14 + 1x + 3x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-14 + 1x + 3x2 = 0

Factor a trinomial.
(-7 + -3x)(2 + -1x) = 0

Subproblem 1
Set the factor '(-7 + -3x)' equal to zero and attempt to solve:

Simplifying
-7 + -3x = 0

Solving
-7 + -3x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -3x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -3x = 0 + 7
-3x = 0 + 7

Combine like terms: 0 + 7 = 7
-3x = 7

Divide each side by '-3'.
x = -2.333333333

Simplifying
x = -2.333333333
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 = {-2.333333333, 2}