x^2-6=4x^2-9x-6

Solution for x^2-6=4x^2-9x-6 equation:

Simplifying
x2 + -6 = 4x2 + -9x + -6

Reorder the terms:
-6 + x2 = 4x2 + -9x + -6

Reorder the terms:
-6 + x2 = -6 + -9x + 4x2

Add '6' to each side of the equation.
-6 + 6 + x2 = -6 + -9x + 6 + 4x2

Combine like terms: -6 + 6 = 0
0 + x2 = -6 + -9x + 6 + 4x2
x2 = -6 + -9x + 6 + 4x2

Reorder the terms:
x2 = -6 + 6 + -9x + 4x2

Combine like terms: -6 + 6 = 0
x2 = 0 + -9x + 4x2
x2 = -9x + 4x2

Solving
x2 = -9x + 4x2

Solving for variable 'x'.

Reorder the terms:
9x + x2 + -4x2 = -9x + 4x2 + 9x + -4x2

Combine like terms: x2 + -4x2 = -3x2
9x + -3x2 = -9x + 4x2 + 9x + -4x2

Reorder the terms:
9x + -3x2 = -9x + 9x + 4x2 + -4x2

Combine like terms: -9x + 9x = 0
9x + -3x2 = 0 + 4x2 + -4x2
9x + -3x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
9x + -3x2 = 0

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

Ignore the factor 3.
Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {0, 3}