60x-3x^2=10x+2x^2

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Solution for 60x-3x^2=10x+2x^2 equation: 


Simplifying
60x + -3x2 = 10x + 2x2

Solving
60x + -3x2 = 10x + 2x2

Solving for variable 'x'.

Reorder the terms:
60x + -10x + -3x2 + -2x2 = 10x + 2x2 + -10x + -2x2

Combine like terms: 60x + -10x = 50x
50x + -3x2 + -2x2 = 10x + 2x2 + -10x + -2x2

Combine like terms: -3x2 + -2x2 = -5x2
50x + -5x2 = 10x + 2x2 + -10x + -2x2

Reorder the terms:
50x + -5x2 = 10x + -10x + 2x2 + -2x2

Combine like terms: 10x + -10x = 0
50x + -5x2 = 0 + 2x2 + -2x2
50x + -5x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
50x + -5x2 = 0

Factor out the Greatest Common Factor (GCF), '5x'.
5x(10 + -1x) = 0

Ignore the factor 5.

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 '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {0, 10}

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