x(x+1)=x(-20-8x)-6

Solution for x(x+1)=x(-20-8x)-6 equation:

Simplifying
x(x + 1) = x(-20 + -8x) + -6

Reorder the terms:
x(1 + x) = x(-20 + -8x) + -6
(1 * x + x * x) = x(-20 + -8x) + -6
(1x + x2) = x(-20 + -8x) + -6
1x + x2 = (-20 * x + -8x * x) + -6
1x + x2 = (-20x + -8x2) + -6

Reorder the terms:
1x + x2 = -6 + -20x + -8x2

Solving
1x + x2 = -6 + -20x + -8x2

Solving for variable 'x'.

Reorder the terms:
6 + 1x + 20x + x2 + 8x2 = -6 + -20x + -8x2 + 6 + 20x + 8x2

Combine like terms: 1x + 20x = 21x
6 + 21x + x2 + 8x2 = -6 + -20x + -8x2 + 6 + 20x + 8x2

Combine like terms: x2 + 8x2 = 9x2
6 + 21x + 9x2 = -6 + -20x + -8x2 + 6 + 20x + 8x2

Reorder the terms:
6 + 21x + 9x2 = -6 + 6 + -20x + 20x + -8x2 + 8x2

Combine like terms: -6 + 6 = 0
6 + 21x + 9x2 = 0 + -20x + 20x + -8x2 + 8x2
6 + 21x + 9x2 = -20x + 20x + -8x2 + 8x2

Combine like terms: -20x + 20x = 0
6 + 21x + 9x2 = 0 + -8x2 + 8x2
6 + 21x + 9x2 = -8x2 + 8x2

Combine like terms: -8x2 + 8x2 = 0
6 + 21x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + 7x + 3x2) = 0

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

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

Simplifying
2 + x = 0

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

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

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

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

Simplifying
1 + 3x = 0

Solving
1 + 3x = 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 + 3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3x = 0 + -1
3x = 0 + -1

Combine like terms: 0 + -1 = -1
3x = -1

Divide each side by '3'.
x = -0.3333333333

Simplifying
x = -0.3333333333
Solution
x = {-2, -0.3333333333}