2(x+1)(x+5)-10=0

Solution for 2(x+1)(x+5)-10=0 equation:

Simplifying
2(x + 1)(x + 5) + -10 = 0

Reorder the terms:
2(1 + x)(x + 5) + -10 = 0

Reorder the terms:
2(1 + x)(5 + x) + -10 = 0

Multiply (1 + x) * (5 + x)
2(1(5 + x) + x(5 + x)) + -10 = 0
2((5 * 1 + x * 1) + x(5 + x)) + -10 = 0
2((5 + 1x) + x(5 + x)) + -10 = 0
2(5 + 1x + (5 * x + x * x)) + -10 = 0
2(5 + 1x + (5x + x2)) + -10 = 0

Combine like terms: 1x + 5x = 6x
2(5 + 6x + x2) + -10 = 0
(5 * 2 + 6x * 2 + x2 * 2) + -10 = 0
(10 + 12x + 2x2) + -10 = 0

Reorder the terms:
10 + -10 + 12x + 2x2 = 0

Combine like terms: 10 + -10 = 0
0 + 12x + 2x2 = 0
12x + 2x2 = 0

Solving
12x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(6 + x) = 0

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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

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

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

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

Simplifying
x = -6
Solution
x = {0, -6}