(2x+1)(x-1)=14

Solution for (2x+1)(x-1)=14 equation:

Simplifying
(2x + 1)(x + -1) = 14

Reorder the terms:
(1 + 2x)(x + -1) = 14

Reorder the terms:
(1 + 2x)(-1 + x) = 14

Multiply (1 + 2x) * (-1 + x)
(1(-1 + x) + 2x * (-1 + x)) = 14
((-1 * 1 + x * 1) + 2x * (-1 + x)) = 14
((-1 + 1x) + 2x * (-1 + x)) = 14
(-1 + 1x + (-1 * 2x + x * 2x)) = 14
(-1 + 1x + (-2x + 2x2)) = 14

Combine like terms: 1x + -2x = -1x
(-1 + -1x + 2x2) = 14

Solving
-1 + -1x + 2x2 = 14

Solving for variable 'x'.

Reorder the terms:
-1 + -14 + -1x + 2x2 = 14 + -14

Combine like terms: -1 + -14 = -15
-15 + -1x + 2x2 = 14 + -14

Combine like terms: 14 + -14 = 0
-15 + -1x + 2x2 = 0

Factor a trinomial.
(-5 + -2x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-5 + -2x)' equal to zero and attempt to solve:

Simplifying
-5 + -2x = 0

Solving
-5 + -2x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -2x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2x = 0 + 5
-2x = 0 + 5

Combine like terms: 0 + 5 = 5
-2x = 5

Divide each side by '-2'.
x = -2.5

Simplifying
x = -2.5
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 = {-2.5, 3}