x^2=15x-2x^2

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


Simplifying
x2 = 15x + -2x2

Solving
x2 = 15x + -2x2

Solving for variable 'x'.

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-5 + x) = 0

Ignore the factor 3.

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 + x)' equal to zero and attempt to solve: Simplifying -5 + x = 0 Solving -5 + x = 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 + x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + x = 0 + 5 x = 0 + 5 Combine like terms: 0 + 5 = 5 x = 5 Simplifying x = 5

Solution

x = {0, 5}

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