-3x(9x+5)=-6(3x+10)

Solution for -3x(9x+5)=-6(3x+10) equation:

Simplifying
-3x(9x + 5) = -6(3x + 10)

Reorder the terms:
-3x(5 + 9x) = -6(3x + 10)
(5 * -3x + 9x * -3x) = -6(3x + 10)
(-15x + -27x2) = -6(3x + 10)

Reorder the terms:
-15x + -27x2 = -6(10 + 3x)
-15x + -27x2 = (10 * -6 + 3x * -6)
-15x + -27x2 = (-60 + -18x)

Solving
-15x + -27x2 = -60 + -18x

Solving for variable 'x'.

Reorder the terms:
60 + -15x + 18x + -27x2 = -60 + -18x + 60 + 18x

Combine like terms: -15x + 18x = 3x
60 + 3x + -27x2 = -60 + -18x + 60 + 18x

Reorder the terms:
60 + 3x + -27x2 = -60 + 60 + -18x + 18x

Combine like terms: -60 + 60 = 0
60 + 3x + -27x2 = 0 + -18x + 18x
60 + 3x + -27x2 = -18x + 18x

Combine like terms: -18x + 18x = 0
60 + 3x + -27x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(20 + x + -9x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(20 + x + -9x2)' equal to zero and attempt to solve:

Simplifying
20 + x + -9x2 = 0

Solving
20 + x + -9x2 = 0

Begin completing the square.  Divide all terms by
-9 the coefficient of the squared term: 

Divide each side by '-9'.
-2.222222222 + -0.1111111111x + x2 = 0

Move the constant term to the right:

Add '2.222222222' to each side of the equation.
-2.222222222 + -0.1111111111x + 2.222222222 + x2 = 0 + 2.222222222

Reorder the terms:
-2.222222222 + 2.222222222 + -0.1111111111x + x2 = 0 + 2.222222222

Combine like terms: -2.222222222 + 2.222222222 = 0.000000000
0.000000000 + -0.1111111111x + x2 = 0 + 2.222222222
-0.1111111111x + x2 = 0 + 2.222222222

Combine like terms: 0 + 2.222222222 = 2.222222222
-0.1111111111x + x2 = 2.222222222

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-0.1111111111x + 0.25 + x2 = 2.222222222 + 0.25

Reorder the terms:
0.25 + -0.1111111111x + x2 = 2.222222222 + 0.25

Combine like terms: 2.222222222 + 0.25 = 2.472222222
0.25 + -0.1111111111x + x2 = 2.472222222

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 2.472222222

Calculate the square root of the right side: 1.572330189

Break this problem into two subproblems by setting 
(x + 0.5) equal to 1.572330189 and -1.572330189.

Subproblem 1
x + 0.5 = 1.572330189

Simplifying
x + 0.5 = 1.572330189

Reorder the terms:
0.5 + x = 1.572330189

Solving
0.5 + x = 1.572330189

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 1.572330189 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 1.572330189 + -0.5
x = 1.572330189 + -0.5

Combine like terms: 1.572330189 + -0.5 = 1.072330189
x = 1.072330189

Simplifying
x = 1.072330189

Subproblem 2
x + 0.5 = -1.572330189

Simplifying
x + 0.5 = -1.572330189

Reorder the terms:
0.5 + x = -1.572330189

Solving
0.5 + x = -1.572330189

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -1.572330189 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -1.572330189 + -0.5
x = -1.572330189 + -0.5

Combine like terms: -1.572330189 + -0.5 = -2.072330189
x = -2.072330189

Simplifying
x = -2.072330189

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.072330189, -2.072330189}
Solution
x = {1.072330189, -2.072330189}