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

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

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

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

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

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

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

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

Solving for variable 'x'.

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

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

Combine like terms: 5 + -5 = 0
-6 + -1x + 2x2 = 0

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

Subproblem 1
Set the factor '(-3 + -2x)' equal to zero and attempt to solve:

Simplifying
-3 + -2x = 0

Solving
-3 + -2x = 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 + -2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2x = 0 + 3
-2x = 0 + 3

Combine like terms: 0 + 3 = 3
-2x = 3

Divide each side by '-2'.
x = -1.5

Simplifying
x = -1.5
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 = {-1.5, 2}