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

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


Simplifying
8x2 + -3x = 2x2 + x

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

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

Solving
-3x + 8x2 = x + 2x2

Solving for variable 'x'.

Reorder the terms:
-3x + -1x + 8x2 + -2x2 = x + 2x2 + -1x + -2x2

Combine like terms: -3x + -1x = -4x
-4x + 8x2 + -2x2 = x + 2x2 + -1x + -2x2

Combine like terms: 8x2 + -2x2 = 6x2
-4x + 6x2 = x + 2x2 + -1x + -2x2

Reorder the terms:
-4x + 6x2 = x + -1x + 2x2 + -2x2

Combine like terms: x + -1x = 0
-4x + 6x2 = 0 + 2x2 + -2x2
-4x + 6x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-4x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-2 + 3x) = 0

Ignore the factor 2.

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 '(-2 + 3x)' equal to zero and attempt to solve:

Simplifying
-2 + 3x = 0

Solving
-2 + 3x = 0

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

Add '2' to each side of the equation.
-2 + 2 + 3x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 3x = 0 + 2
3x = 0 + 2

Combine like terms: 0 + 2 = 2
3x = 2

Divide each side by '3'.
x = 0.6666666667

Simplifying
x = 0.6666666667
Solution
x = {0, 0.6666666667}

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