10x^2-3x=-2x^2+36

Solution for 10x^2-3x=-2x^2+36 equation:

Simplifying
10x2 + -3x = -2x2 + 36

Reorder the terms:
-3x + 10x2 = -2x2 + 36

Reorder the terms:
-3x + 10x2 = 36 + -2x2

Solving
-3x + 10x2 = 36 + -2x2

Solving for variable 'x'.

Reorder the terms:
-36 + -3x + 10x2 + 2x2 = 36 + -2x2 + -36 + 2x2

Combine like terms: 10x2 + 2x2 = 12x2
-36 + -3x + 12x2 = 36 + -2x2 + -36 + 2x2

Reorder the terms:
-36 + -3x + 12x2 = 36 + -36 + -2x2 + 2x2

Combine like terms: 36 + -36 = 0
-36 + -3x + 12x2 = 0 + -2x2 + 2x2
-36 + -3x + 12x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
-36 + -3x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-12 + -1x + 4x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-12 + -1x + 4x2)' equal to zero and attempt to solve:

Simplifying
-12 + -1x + 4x2 = 0

Solving
-12 + -1x + 4x2 = 0

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

Divide each side by '4'.
-3 + -0.25x + x2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -0.25x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + -0.25x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -0.25x + x2 = 0 + 3
-0.25x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
-0.25x + x2 = 3

The x term is -0.25x.  Take half its coefficient (-0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
-0.25x + 0.015625 + x2 = 3 + 0.015625

Reorder the terms:
0.015625 + -0.25x + x2 = 3 + 0.015625

Combine like terms: 3 + 0.015625 = 3.015625
0.015625 + -0.25x + x2 = 3.015625

Factor a perfect square on the left side:
(x + -0.125)(x + -0.125) = 3.015625

Calculate the square root of the right side: 1.736555499

Break this problem into two subproblems by setting 
(x + -0.125) equal to 1.736555499 and -1.736555499.

Subproblem 1
x + -0.125 = 1.736555499

Simplifying
x + -0.125 = 1.736555499

Reorder the terms:
-0.125 + x = 1.736555499

Solving
-0.125 + x = 1.736555499

Solving for variable 'x'.

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

Add '0.125' to each side of the equation.
-0.125 + 0.125 + x = 1.736555499 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + x = 1.736555499 + 0.125
x = 1.736555499 + 0.125

Combine like terms: 1.736555499 + 0.125 = 1.861555499
x = 1.861555499

Simplifying
x = 1.861555499

Subproblem 2
x + -0.125 = -1.736555499

Simplifying
x + -0.125 = -1.736555499

Reorder the terms:
-0.125 + x = -1.736555499

Solving
-0.125 + x = -1.736555499

Solving for variable 'x'.

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

Add '0.125' to each side of the equation.
-0.125 + 0.125 + x = -1.736555499 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + x = -1.736555499 + 0.125
x = -1.736555499 + 0.125

Combine like terms: -1.736555499 + 0.125 = -1.611555499
x = -1.611555499

Simplifying
x = -1.611555499

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.861555499, -1.611555499}
Solution
x = {1.861555499, -1.611555499}