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

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


Simplifying
-2x2 + 15x = -1x2 + 10x

Reorder the terms:
15x + -2x2 = -1x2 + 10x

Reorder the terms:
15x + -2x2 = 10x + -1x2

Solving
15x + -2x2 = 10x + -1x2

Solving for variable 'x'.

Reorder the terms:
15x + -10x + -2x2 + x2 = 10x + -1x2 + -10x + x2

Combine like terms: 15x + -10x = 5x
5x + -2x2 + x2 = 10x + -1x2 + -10x + x2

Combine like terms: -2x2 + x2 = -1x2
5x + -1x2 = 10x + -1x2 + -10x + x2

Reorder the terms:
5x + -1x2 = 10x + -10x + -1x2 + x2

Combine like terms: 10x + -10x = 0
5x + -1x2 = 0 + -1x2 + x2
5x + -1x2 = -1x2 + x2

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(5 + -1x) = 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 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 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 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5

Solution

x = {0, 5}

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