5x(x+10)=15-10x+20

Solution for 5x(x+10)=15-10x+20 equation:

Simplifying
5x(x + 10) = 15 + -10x + 20

Reorder the terms:
5x(10 + x) = 15 + -10x + 20
(10 * 5x + x * 5x) = 15 + -10x + 20
(50x + 5x2) = 15 + -10x + 20

Reorder the terms:
50x + 5x2 = 15 + 20 + -10x

Combine like terms: 15 + 20 = 35
50x + 5x2 = 35 + -10x

Solving
50x + 5x2 = 35 + -10x

Solving for variable 'x'.

Reorder the terms:
-35 + 50x + 10x + 5x2 = 35 + -10x + -35 + 10x

Combine like terms: 50x + 10x = 60x
-35 + 60x + 5x2 = 35 + -10x + -35 + 10x

Reorder the terms:
-35 + 60x + 5x2 = 35 + -35 + -10x + 10x

Combine like terms: 35 + -35 = 0
-35 + 60x + 5x2 = 0 + -10x + 10x
-35 + 60x + 5x2 = -10x + 10x

Combine like terms: -10x + 10x = 0
-35 + 60x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-7 + 12x + x2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-7 + 12x + x2)' equal to zero and attempt to solve:

Simplifying
-7 + 12x + x2 = 0

Solving
-7 + 12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + 12x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + 12x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 12x + x2 = 0 + 7
12x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
12x + x2 = 7

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = 7 + 36

Reorder the terms:
36 + 12x + x2 = 7 + 36

Combine like terms: 7 + 36 = 43
36 + 12x + x2 = 43

Factor a perfect square on the left side:
(x + 6)(x + 6) = 43

Calculate the square root of the right side: 6.557438524

Break this problem into two subproblems by setting 
(x + 6) equal to 6.557438524 and -6.557438524.

Subproblem 1
x + 6 = 6.557438524

Simplifying
x + 6 = 6.557438524

Reorder the terms:
6 + x = 6.557438524

Solving
6 + x = 6.557438524

Solving for variable 'x'.

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 = 6.557438524 + -6

Combine like terms: 6 + -6 = 0
0 + x = 6.557438524 + -6
x = 6.557438524 + -6

Combine like terms: 6.557438524 + -6 = 0.557438524
x = 0.557438524

Simplifying
x = 0.557438524

Subproblem 2
x + 6 = -6.557438524

Simplifying
x + 6 = -6.557438524

Reorder the terms:
6 + x = -6.557438524

Solving
6 + x = -6.557438524

Solving for variable 'x'.

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 = -6.557438524 + -6

Combine like terms: 6 + -6 = 0
0 + x = -6.557438524 + -6
x = -6.557438524 + -6

Combine like terms: -6.557438524 + -6 = -12.557438524
x = -12.557438524

Simplifying
x = -12.557438524

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.557438524, -12.557438524}
Solution
x = {0.557438524, -12.557438524}