5x^2-2x-6=-3x^2+6

Solution for 5x^2-2x-6=-3x^2+6 equation:

Simplifying
5x2 + -2x + -6 = -3x2 + 6

Reorder the terms:
-6 + -2x + 5x2 = -3x2 + 6

Reorder the terms:
-6 + -2x + 5x2 = 6 + -3x2

Solving
-6 + -2x + 5x2 = 6 + -3x2

Solving for variable 'x'.

Reorder the terms:
-6 + -6 + -2x + 5x2 + 3x2 = 6 + -3x2 + -6 + 3x2

Combine like terms: -6 + -6 = -12
-12 + -2x + 5x2 + 3x2 = 6 + -3x2 + -6 + 3x2

Combine like terms: 5x2 + 3x2 = 8x2
-12 + -2x + 8x2 = 6 + -3x2 + -6 + 3x2

Reorder the terms:
-12 + -2x + 8x2 = 6 + -6 + -3x2 + 3x2

Combine like terms: 6 + -6 = 0
-12 + -2x + 8x2 = 0 + -3x2 + 3x2
-12 + -2x + 8x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
-12 + -2x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + -1x + 4x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-6 + -1x + 4x2)' equal to zero and attempt to solve:

Simplifying
-6 + -1x + 4x2 = 0

Solving
-6 + -1x + 4x2 = 0

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

Divide each side by '4'.
-1.5 + -0.25x + x2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + -0.25x + 1.5 + x2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + -0.25x + x2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + -0.25x + x2 = 0 + 1.5
-0.25x + x2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
-0.25x + x2 = 1.5

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 = 1.5 + 0.015625

Reorder the terms:
0.015625 + -0.25x + x2 = 1.5 + 0.015625

Combine like terms: 1.5 + 0.015625 = 1.515625
0.015625 + -0.25x + x2 = 1.515625

Factor a perfect square on the left side:
(x + -0.125)(x + -0.125) = 1.515625

Calculate the square root of the right side: 1.231107225

Break this problem into two subproblems by setting 
(x + -0.125) equal to 1.231107225 and -1.231107225.

Subproblem 1
x + -0.125 = 1.231107225

Simplifying
x + -0.125 = 1.231107225

Reorder the terms:
-0.125 + x = 1.231107225

Solving
-0.125 + x = 1.231107225

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 = 1.231107225 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + x = 1.231107225 + 0.125
x = 1.231107225 + 0.125

Combine like terms: 1.231107225 + 0.125 = 1.356107225
x = 1.356107225

Simplifying
x = 1.356107225

Subproblem 2
x + -0.125 = -1.231107225

Simplifying
x + -0.125 = -1.231107225

Reorder the terms:
-0.125 + x = -1.231107225

Solving
-0.125 + x = -1.231107225

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 = -1.231107225 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + x = -1.231107225 + 0.125
x = -1.231107225 + 0.125

Combine like terms: -1.231107225 + 0.125 = -1.106107225
x = -1.106107225

Simplifying
x = -1.106107225

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.356107225, -1.106107225}
Solution
x = {1.356107225, -1.106107225}