5(x+6)-3x=-2x(x+9)

Solution for 5(x+6)-3x=-2x(x+9) equation:

Simplifying
5(x + 6) + -3x = -2x(x + 9)

Reorder the terms:
5(6 + x) + -3x = -2x(x + 9)
(6 * 5 + x * 5) + -3x = -2x(x + 9)
(30 + 5x) + -3x = -2x(x + 9)

Combine like terms: 5x + -3x = 2x
30 + 2x = -2x(x + 9)

Reorder the terms:
30 + 2x = -2x(9 + x)
30 + 2x = (9 * -2x + x * -2x)
30 + 2x = (-18x + -2x2)

Solving
30 + 2x = -18x + -2x2

Solving for variable 'x'.

Combine like terms: 2x + 18x = 20x
30 + 20x + 2x2 = -18x + -2x2 + 18x + 2x2

Reorder the terms:
30 + 20x + 2x2 = -18x + 18x + -2x2 + 2x2

Combine like terms: -18x + 18x = 0
30 + 20x + 2x2 = 0 + -2x2 + 2x2
30 + 20x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
30 + 20x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(15 + 10x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(15 + 10x + x2)' equal to zero and attempt to solve:

Simplifying
15 + 10x + x2 = 0

Solving
15 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + 10x + -15 + x2 = 0 + -15

Reorder the terms:
15 + -15 + 10x + x2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + 10x + x2 = 0 + -15
10x + x2 = 0 + -15

Combine like terms: 0 + -15 = -15
10x + x2 = -15

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = -15 + 25

Reorder the terms:
25 + 10x + x2 = -15 + 25

Combine like terms: -15 + 25 = 10
25 + 10x + x2 = 10

Factor a perfect square on the left side:
(x + 5)(x + 5) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(x + 5) equal to 3.16227766 and -3.16227766.

Subproblem 1
x + 5 = 3.16227766

Simplifying
x + 5 = 3.16227766

Reorder the terms:
5 + x = 3.16227766

Solving
5 + x = 3.16227766

Solving for variable 'x'.

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 = 3.16227766 + -5

Combine like terms: 5 + -5 = 0
0 + x = 3.16227766 + -5
x = 3.16227766 + -5

Combine like terms: 3.16227766 + -5 = -1.83772234
x = -1.83772234

Simplifying
x = -1.83772234

Subproblem 2
x + 5 = -3.16227766

Simplifying
x + 5 = -3.16227766

Reorder the terms:
5 + x = -3.16227766

Solving
5 + x = -3.16227766

Solving for variable 'x'.

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 = -3.16227766 + -5

Combine like terms: 5 + -5 = 0
0 + x = -3.16227766 + -5
x = -3.16227766 + -5

Combine like terms: -3.16227766 + -5 = -8.16227766
x = -8.16227766

Simplifying
x = -8.16227766

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.83772234, -8.16227766}
Solution
x = {-1.83772234, -8.16227766}