(2x+1)(x+1)=15

Solution for (2x+1)(x+1)=15 equation:

Simplifying
(2x + 1)(x + 1) = 15

Reorder the terms:
(1 + 2x)(x + 1) = 15

Reorder the terms:
(1 + 2x)(1 + x) = 15

Multiply (1 + 2x) * (1 + x)
(1(1 + x) + 2x * (1 + x)) = 15
((1 * 1 + x * 1) + 2x * (1 + x)) = 15
((1 + 1x) + 2x * (1 + x)) = 15
(1 + 1x + (1 * 2x + x * 2x)) = 15
(1 + 1x + (2x + 2x2)) = 15

Combine like terms: 1x + 2x = 3x
(1 + 3x + 2x2) = 15

Solving
1 + 3x + 2x2 = 15

Solving for variable 'x'.

Reorder the terms:
1 + -15 + 3x + 2x2 = 15 + -15

Combine like terms: 1 + -15 = -14
-14 + 3x + 2x2 = 15 + -15

Combine like terms: 15 + -15 = 0
-14 + 3x + 2x2 = 0

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

Subproblem 1
Set the factor '(-7 + -2x)' equal to zero and attempt to solve:

Simplifying
-7 + -2x = 0

Solving
-7 + -2x = 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 + -2x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2x = 0 + 7
-2x = 0 + 7

Combine like terms: 0 + 7 = 7
-2x = 7

Divide each side by '-2'.
x = -3.5

Simplifying
x = -3.5
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 = {-3.5, 2}