8x^2-19x=2x^2-x

Solution for 8x^2-19x=2x^2-x equation:

Simplifying
8x2 + -19x = 2x2 + -1x

Reorder the terms:
-19x + 8x2 = 2x2 + -1x

Reorder the terms:
-19x + 8x2 = -1x + 2x2

Solving
-19x + 8x2 = -1x + 2x2

Solving for variable 'x'.

Reorder the terms:
-19x + x + 8x2 + -2x2 = -1x + 2x2 + x + -2x2

Combine like terms: -19x + x = -18x
-18x + 8x2 + -2x2 = -1x + 2x2 + x + -2x2

Combine like terms: 8x2 + -2x2 = 6x2
-18x + 6x2 = -1x + 2x2 + x + -2x2

Reorder the terms:
-18x + 6x2 = -1x + x + 2x2 + -2x2

Combine like terms: -1x + x = 0
-18x + 6x2 = 0 + 2x2 + -2x2
-18x + 6x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-18x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '6x'.
6x(-3 + x) = 0

Ignore the factor 6.
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}