26x^2=60x-2x^3

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Solution for 26x^2=60x-2x^3 equation:


Simplifying
26x2 = 60x + -2x3

Solving
26x2 = 60x + -2x3

Solving for variable 'x'.

Reorder the terms:
-60x + 26x2 + 2x3 = 60x + -2x3 + -60x + 2x3

Reorder the terms:
-60x + 26x2 + 2x3 = 60x + -60x + -2x3 + 2x3

Combine like terms: 60x + -60x = 0
-60x + 26x2 + 2x3 = 0 + -2x3 + 2x3
-60x + 26x2 + 2x3 = -2x3 + 2x3

Combine like terms: -2x3 + 2x3 = 0
-60x + 26x2 + 2x3 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-30 + 13x + x2) = 0

Factor a trinomial.
2x((-15 + -1x)(2 + -1x)) = 0

Ignore the factor 2.

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 '(-15 + -1x)' equal to zero and attempt to solve: Simplifying -15 + -1x = 0 Solving -15 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + -1x = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -1x = 0 + 15 -1x = 0 + 15 Combine like terms: 0 + 15 = 15 -1x = 15 Divide each side by '-1'. x = -15 Simplifying x = -15

Subproblem 3

Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2

Solution

x = {0, -15, 2}

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