4(x+5)+8(x^2+10x+25)=0

Solution for 4(x+5)+8(x^2+10x+25)=0 equation:

Simplifying
4(x + 5) + 8(x2 + 10x + 25) = 0

Reorder the terms:
4(5 + x) + 8(x2 + 10x + 25) = 0
(5 * 4 + x * 4) + 8(x2 + 10x + 25) = 0
(20 + 4x) + 8(x2 + 10x + 25) = 0

Reorder the terms:
20 + 4x + 8(25 + 10x + x2) = 0
20 + 4x + (25 * 8 + 10x * 8 + x2 * 8) = 0
20 + 4x + (200 + 80x + 8x2) = 0

Reorder the terms:
20 + 200 + 4x + 80x + 8x2 = 0

Combine like terms: 20 + 200 = 220
220 + 4x + 80x + 8x2 = 0

Combine like terms: 4x + 80x = 84x
220 + 84x + 8x2 = 0

Solving
220 + 84x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(55 + 21x + 2x2) = 0

Factor a trinomial.
4((11 + 2x)(5 + x)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(11 + 2x)' equal to zero and attempt to solve:

Simplifying
11 + 2x = 0

Solving
11 + 2x = 0

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

Add '-11' to each side of the equation.
11 + -11 + 2x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 2x = 0 + -11
2x = 0 + -11

Combine like terms: 0 + -11 = -11
2x = -11

Divide each side by '2'.
x = -5.5

Simplifying
x = -5.5
Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

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

Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5
Solution
x = {-5.5, -5}