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

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

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

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

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

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

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

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

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

Solving for variable 'x'.

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

Combine like terms: -1 + -5 = -6
-6 + 1x + -5x + 2x2 = 5 + 5x + -5 + -5x

Combine like terms: 1x + -5x = -4x
-6 + -4x + 2x2 = 5 + 5x + -5 + -5x

Reorder the terms:
-6 + -4x + 2x2 = 5 + -5 + 5x + -5x

Combine like terms: 5 + -5 = 0
-6 + -4x + 2x2 = 0 + 5x + -5x
-6 + -4x + 2x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-6 + -4x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -2x + x2) = 0

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

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

Simplifying
-1 + -1x = 0

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

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

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

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

Simplifying
x = -1
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 = {-1, 3}