3x^2-8x+6=x+6

Solution for 3x^2-8x+6=x+6 equation:

Simplifying
3x2 + -8x + 6 = x + 6

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

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

Add '-6' to each side of the equation.
6 + -8x + -6 + 3x2 = 6 + -6 + x

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

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

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

Solving
-8x + 3x2 = x

Solving for variable 'x'.

Reorder the terms:
-8x + -1x + 3x2 = x + -1x

Combine like terms: -8x + -1x = -9x
-9x + 3x2 = x + -1x

Combine like terms: x + -1x = 0
-9x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-3 + x) = 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 + x)' equal to zero and attempt to solve:

Simplifying
-3 + x = 0

Solving
-3 + x = 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 + x = 0 + 3

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

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

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