(5x^2-6x)-(3x^2-2x)=x

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


Simplifying
(5x2 + -6x) + -1(3x2 + -2x) = x

Reorder the terms:
(-6x + 5x2) + -1(3x2 + -2x) = x

Remove parenthesis around (-6x + 5x2)
-6x + 5x2 + -1(3x2 + -2x) = x

Reorder the terms:
-6x + 5x2 + -1(-2x + 3x2) = x
-6x + 5x2 + (-2x * -1 + 3x2 * -1) = x
-6x + 5x2 + (2x + -3x2) = x

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

Combine like terms: -6x + 2x = -4x
-4x + 5x2 + -3x2 = x

Combine like terms: 5x2 + -3x2 = 2x2
-4x + 2x2 = x

Solving
-4x + 2x2 = x

Solving for variable 'x'.

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

Combine like terms: -4x + -1x = -5x
-5x + 2x2 = x + -1x

Combine like terms: x + -1x = 0
-5x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-5 + 2x) = 0


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 '(-5 + 2x)' equal to zero and attempt to solve:

Simplifying
-5 + 2x = 0

Solving
-5 + 2x = 0

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

Add '5' to each side of the equation.
-5 + 5 + 2x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 2x = 0 + 5
2x = 0 + 5

Combine like terms: 0 + 5 = 5
2x = 5

Divide each side by '2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {0, 2.5}

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