=10x^3-15x^2-10x

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Solution for =10x^3-15x^2-10x equation:


Simplifying
0 = 10x3 + -15x2 + -10x

Reorder the terms:
0 = -10x + -15x2 + 10x3

Solving
0 = -10x + -15x2 + 10x3

Solving for variable 'x'.
Remove the zero:
10x + 15x2 + -10x3 = -10x + -15x2 + 10x3 + 10x + 15x2 + -10x3

Reorder the terms:
10x + 15x2 + -10x3 = -10x + 10x + -15x2 + 15x2 + 10x3 + -10x3

Combine like terms: -10x + 10x = 0
10x + 15x2 + -10x3 = 0 + -15x2 + 15x2 + 10x3 + -10x3
10x + 15x2 + -10x3 = -15x2 + 15x2 + 10x3 + -10x3

Combine like terms: -15x2 + 15x2 = 0
10x + 15x2 + -10x3 = 0 + 10x3 + -10x3
10x + 15x2 + -10x3 = 10x3 + -10x3

Combine like terms: 10x3 + -10x3 = 0
10x + 15x2 + -10x3 = 0

Factor out the Greatest Common Factor (GCF), '5x'.
5x(2 + 3x + -2x2) = 0

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

Ignore the factor 5.

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 '(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

Subproblem 3

Set the factor '(1 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Divide each side by '2'. x = -0.5 Simplifying x = -0.5

Solution

x = {0, 2, -0.5}

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