0=-2x^5+24x^4-70x^3

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Solution for 0=-2x^5+24x^4-70x^3 equation:


Simplifying
0 = -2x5 + 24x4 + -70x3

Reorder the terms:
0 = -70x3 + 24x4 + -2x5

Solving
0 = -70x3 + 24x4 + -2x5

Solving for variable 'x'.
Remove the zero:
70x3 + -24x4 + 2x5 = -70x3 + 24x4 + -2x5 + 70x3 + -24x4 + 2x5

Reorder the terms:
70x3 + -24x4 + 2x5 = -70x3 + 70x3 + 24x4 + -24x4 + -2x5 + 2x5

Combine like terms: -70x3 + 70x3 = 0
70x3 + -24x4 + 2x5 = 0 + 24x4 + -24x4 + -2x5 + 2x5
70x3 + -24x4 + 2x5 = 24x4 + -24x4 + -2x5 + 2x5

Combine like terms: 24x4 + -24x4 = 0
70x3 + -24x4 + 2x5 = 0 + -2x5 + 2x5
70x3 + -24x4 + 2x5 = -2x5 + 2x5

Combine like terms: -2x5 + 2x5 = 0
70x3 + -24x4 + 2x5 = 0

Factor out the Greatest Common Factor (GCF), '2x3'.
2x3(35 + -12x + x2) = 0

Factor a trinomial.
2x3((5 + -1x)(7 + -1x)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor 'x3' equal to zero and attempt to solve: Simplifying x3 = 0 Solving x3 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

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

Subproblem 3

Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7

Solution

x = {5, 7}

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