x^2+10x=15x-2x^2

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Solution for x^2+10x=15x-2x^2 equation: 


Simplifying
x2 + 10x = 15x + -2x2

Reorder the terms:
10x + x2 = 15x + -2x2

Solving
10x + x2 = 15x + -2x2

Solving for variable 'x'.

Reorder the terms:
10x + -15x + x2 + 2x2 = 15x + -2x2 + -15x + 2x2

Combine like terms: 10x + -15x = -5x
-5x + x2 + 2x2 = 15x + -2x2 + -15x + 2x2

Combine like terms: x2 + 2x2 = 3x2
-5x + 3x2 = 15x + -2x2 + -15x + 2x2

Reorder the terms:
-5x + 3x2 = 15x + -15x + -2x2 + 2x2

Combine like terms: 15x + -15x = 0
-5x + 3x2 = 0 + -2x2 + 2x2
-5x + 3x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
-5x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-5 + 3x) = 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 + 3x)' equal to zero and attempt to solve:

Simplifying
-5 + 3x = 0

Solving
-5 + 3x = 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 + 3x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 3x = 0 + 5
3x = 0 + 5

Combine like terms: 0 + 5 = 5
3x = 5

Divide each side by '3'.
x = 1.666666667

Simplifying
x = 1.666666667
Solution
x = {0, 1.666666667}

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