2x(x-9)-3=-3(-7x+3)-9x

Solution for 2x(x-9)-3=-3(-7x+3)-9x equation:

Simplifying
2x(x + -9) + -3 = -3(-7x + 3) + -9x

Reorder the terms:
2x(-9 + x) + -3 = -3(-7x + 3) + -9x
(-9 * 2x + x * 2x) + -3 = -3(-7x + 3) + -9x
(-18x + 2x2) + -3 = -3(-7x + 3) + -9x

Reorder the terms:
-3 + -18x + 2x2 = -3(-7x + 3) + -9x

Reorder the terms:
-3 + -18x + 2x2 = -3(3 + -7x) + -9x
-3 + -18x + 2x2 = (3 * -3 + -7x * -3) + -9x
-3 + -18x + 2x2 = (-9 + 21x) + -9x

Combine like terms: 21x + -9x = 12x
-3 + -18x + 2x2 = -9 + 12x

Solving
-3 + -18x + 2x2 = -9 + 12x

Solving for variable 'x'.

Reorder the terms:
-3 + 9 + -18x + -12x + 2x2 = -9 + 12x + 9 + -12x

Combine like terms: -3 + 9 = 6
6 + -18x + -12x + 2x2 = -9 + 12x + 9 + -12x

Combine like terms: -18x + -12x = -30x
6 + -30x + 2x2 = -9 + 12x + 9 + -12x

Reorder the terms:
6 + -30x + 2x2 = -9 + 9 + 12x + -12x

Combine like terms: -9 + 9 = 0
6 + -30x + 2x2 = 0 + 12x + -12x
6 + -30x + 2x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
6 + -30x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -15x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -15x + x2)' equal to zero and attempt to solve:

Simplifying
3 + -15x + x2 = 0

Solving
3 + -15x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -15x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + -15x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -15x + x2 = 0 + -3
-15x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-15x + x2 = -3

The x term is -15x.  Take half its coefficient (-7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
-15x + 56.25 + x2 = -3 + 56.25

Reorder the terms:
56.25 + -15x + x2 = -3 + 56.25

Combine like terms: -3 + 56.25 = 53.25
56.25 + -15x + x2 = 53.25

Factor a perfect square on the left side:
(x + -7.5)(x + -7.5) = 53.25

Calculate the square root of the right side: 7.29725976

Break this problem into two subproblems by setting 
(x + -7.5) equal to 7.29725976 and -7.29725976.

Subproblem 1
x + -7.5 = 7.29725976

Simplifying
x + -7.5 = 7.29725976

Reorder the terms:
-7.5 + x = 7.29725976

Solving
-7.5 + x = 7.29725976

Solving for variable 'x'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + x = 7.29725976 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + x = 7.29725976 + 7.5
x = 7.29725976 + 7.5

Combine like terms: 7.29725976 + 7.5 = 14.79725976
x = 14.79725976

Simplifying
x = 14.79725976

Subproblem 2
x + -7.5 = -7.29725976

Simplifying
x + -7.5 = -7.29725976

Reorder the terms:
-7.5 + x = -7.29725976

Solving
-7.5 + x = -7.29725976

Solving for variable 'x'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + x = -7.29725976 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + x = -7.29725976 + 7.5
x = -7.29725976 + 7.5

Combine like terms: -7.29725976 + 7.5 = 0.20274024
x = 0.20274024

Simplifying
x = 0.20274024

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.79725976, 0.20274024}
Solution
x = {14.79725976, 0.20274024}