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

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

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

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

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

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

Combine like terms: 3x + -2x = 1x
(-3 + 1x + 2x2) = x + 5

Reorder the terms:
-3 + 1x + 2x2 = 5 + x

Solving
-3 + 1x + 2x2 = 5 + x

Solving for variable 'x'.

Reorder the terms:
-3 + -5 + 1x + -1x + 2x2 = 5 + x + -5 + -1x

Combine like terms: -3 + -5 = -8
-8 + 1x + -1x + 2x2 = 5 + x + -5 + -1x

Combine like terms: 1x + -1x = 0
-8 + 0 + 2x2 = 5 + x + -5 + -1x
-8 + 2x2 = 5 + x + -5 + -1x

Reorder the terms:
-8 + 2x2 = 5 + -5 + x + -1x

Combine like terms: 5 + -5 = 0
-8 + 2x2 = 0 + x + -1x
-8 + 2x2 = x + -1x

Combine like terms: x + -1x = 0
-8 + 2x2 = 0

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

Factor a difference between two squares.
2((2 + x)(-2 + x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

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

Simplifying
-2 + x = 0

Solving
-2 + x = 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 + x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + x = 0 + 2
x = 0 + 2

Combine like terms: 0 + 2 = 2
x = 2

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