(2x+1)(2x+1)-9=40

Solution for (2x+1)(2x+1)-9=40 equation:

Simplifying
(2x + 1)(2x + 1) + -9 = 40

Reorder the terms:
(1 + 2x)(2x + 1) + -9 = 40

Reorder the terms:
(1 + 2x)(1 + 2x) + -9 = 40

Multiply (1 + 2x) * (1 + 2x)
(1(1 + 2x) + 2x * (1 + 2x)) + -9 = 40
((1 * 1 + 2x * 1) + 2x * (1 + 2x)) + -9 = 40
((1 + 2x) + 2x * (1 + 2x)) + -9 = 40
(1 + 2x + (1 * 2x + 2x * 2x)) + -9 = 40
(1 + 2x + (2x + 4x2)) + -9 = 40

Combine like terms: 2x + 2x = 4x
(1 + 4x + 4x2) + -9 = 40

Reorder the terms:
1 + -9 + 4x + 4x2 = 40

Combine like terms: 1 + -9 = -8
-8 + 4x + 4x2 = 40

Solving
-8 + 4x + 4x2 = 40

Solving for variable 'x'.

Reorder the terms:
-8 + -40 + 4x + 4x2 = 40 + -40

Combine like terms: -8 + -40 = -48
-48 + 4x + 4x2 = 40 + -40

Combine like terms: 40 + -40 = 0
-48 + 4x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-12 + x + x2) = 0

Factor a trinomial.
4((-4 + -1x)(3 + -1x)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4
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 = {-4, 3}