9(x-3)-15(2x-5)x=

Solution for 9(x-3)-15(2x-5)x= equation:

Simplifying
9(x + -3) + -15(2x + -5) * x = 0

Reorder the terms:
9(-3 + x) + -15(2x + -5) * x = 0
(-3 * 9 + x * 9) + -15(2x + -5) * x = 0
(-27 + 9x) + -15(2x + -5) * x = 0

Reorder the terms:
-27 + 9x + -15(-5 + 2x) * x = 0

Reorder the terms for easier multiplication:
-27 + 9x + -15x(-5 + 2x) = 0
-27 + 9x + (-5 * -15x + 2x * -15x) = 0
-27 + 9x + (75x + -30x2) = 0

Combine like terms: 9x + 75x = 84x
-27 + 84x + -30x2 = 0

Solving
-27 + 84x + -30x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-9 + 28x + -10x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-9 + 28x + -10x2)' equal to zero and attempt to solve:

Simplifying
-9 + 28x + -10x2 = 0

Solving
-9 + 28x + -10x2 = 0

Begin completing the square.  Divide all terms by
-10 the coefficient of the squared term: 

Divide each side by '-10'.
0.9 + -2.8x + x2 = 0.0

Move the constant term to the right:

Add '-0.9' to each side of the equation.
0.9 + -2.8x + -0.9 + x2 = 0.0 + -0.9

Reorder the terms:
0.9 + -0.9 + -2.8x + x2 = 0.0 + -0.9

Combine like terms: 0.9 + -0.9 = 0.0
0.0 + -2.8x + x2 = 0.0 + -0.9
-2.8x + x2 = 0.0 + -0.9

Combine like terms: 0.0 + -0.9 = -0.9
-2.8x + x2 = -0.9

The x term is -2.8x.  Take half its coefficient (-1.4).
Square it (1.96) and add it to both sides.

Add '1.96' to each side of the equation.
-2.8x + 1.96 + x2 = -0.9 + 1.96

Reorder the terms:
1.96 + -2.8x + x2 = -0.9 + 1.96

Combine like terms: -0.9 + 1.96 = 1.06
1.96 + -2.8x + x2 = 1.06

Factor a perfect square on the left side:
(x + -1.4)(x + -1.4) = 1.06

Calculate the square root of the right side: 1.029563014

Break this problem into two subproblems by setting 
(x + -1.4) equal to 1.029563014 and -1.029563014.

Subproblem 1
x + -1.4 = 1.029563014

Simplifying
x + -1.4 = 1.029563014

Reorder the terms:
-1.4 + x = 1.029563014

Solving
-1.4 + x = 1.029563014

Solving for variable 'x'.

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

Add '1.4' to each side of the equation.
-1.4 + 1.4 + x = 1.029563014 + 1.4

Combine like terms: -1.4 + 1.4 = 0.0
0.0 + x = 1.029563014 + 1.4
x = 1.029563014 + 1.4

Combine like terms: 1.029563014 + 1.4 = 2.429563014
x = 2.429563014

Simplifying
x = 2.429563014

Subproblem 2
x + -1.4 = -1.029563014

Simplifying
x + -1.4 = -1.029563014

Reorder the terms:
-1.4 + x = -1.029563014

Solving
-1.4 + x = -1.029563014

Solving for variable 'x'.

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

Add '1.4' to each side of the equation.
-1.4 + 1.4 + x = -1.029563014 + 1.4

Combine like terms: -1.4 + 1.4 = 0.0
0.0 + x = -1.029563014 + 1.4
x = -1.029563014 + 1.4

Combine like terms: -1.029563014 + 1.4 = 0.370436986
x = 0.370436986

Simplifying
x = 0.370436986

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.429563014, 0.370436986}
Solution
x = {2.429563014, 0.370436986}