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

Solution for 6(x+2)(x+2)-5(x+2)=1 equation:

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

Reorder the terms:
6(2 + x)(x + 2) + -5(x + 2) = 1

Reorder the terms:
6(2 + x)(2 + x) + -5(x + 2) = 1

Multiply (2 + x) * (2 + x)
6(2(2 + x) + x(2 + x)) + -5(x + 2) = 1
6((2 * 2 + x * 2) + x(2 + x)) + -5(x + 2) = 1
6((4 + 2x) + x(2 + x)) + -5(x + 2) = 1
6(4 + 2x + (2 * x + x * x)) + -5(x + 2) = 1
6(4 + 2x + (2x + x2)) + -5(x + 2) = 1

Combine like terms: 2x + 2x = 4x
6(4 + 4x + x2) + -5(x + 2) = 1
(4 * 6 + 4x * 6 + x2 * 6) + -5(x + 2) = 1
(24 + 24x + 6x2) + -5(x + 2) = 1

Reorder the terms:
24 + 24x + 6x2 + -5(2 + x) = 1
24 + 24x + 6x2 + (2 * -5 + x * -5) = 1
24 + 24x + 6x2 + (-10 + -5x) = 1

Reorder the terms:
24 + -10 + 24x + -5x + 6x2 = 1

Combine like terms: 24 + -10 = 14
14 + 24x + -5x + 6x2 = 1

Combine like terms: 24x + -5x = 19x
14 + 19x + 6x2 = 1

Solving
14 + 19x + 6x2 = 1

Solving for variable 'x'.

Reorder the terms:
14 + -1 + 19x + 6x2 = 1 + -1

Combine like terms: 14 + -1 = 13
13 + 19x + 6x2 = 1 + -1

Combine like terms: 1 + -1 = 0
13 + 19x + 6x2 = 0

Factor a trinomial.
(13 + 6x)(1 + x) = 0

Subproblem 1
Set the factor '(13 + 6x)' equal to zero and attempt to solve:

Simplifying
13 + 6x = 0

Solving
13 + 6x = 0

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

Add '-13' to each side of the equation.
13 + -13 + 6x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + 6x = 0 + -13
6x = 0 + -13

Combine like terms: 0 + -13 = -13
6x = -13

Divide each side by '6'.
x = -2.166666667

Simplifying
x = -2.166666667
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Solution
x = {-2.166666667, -1}