=12x^3-52x^2-40x

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Solution for =12x^3-52x^2-40x equation:


Simplifying
0 = 12x3 + -52x2 + -40x

Reorder the terms:
0 = -40x + -52x2 + 12x3

Solving
0 = -40x + -52x2 + 12x3

Solving for variable 'x'.
Remove the zero:
40x + 52x2 + -12x3 = -40x + -52x2 + 12x3 + 40x + 52x2 + -12x3

Reorder the terms:
40x + 52x2 + -12x3 = -40x + 40x + -52x2 + 52x2 + 12x3 + -12x3

Combine like terms: -40x + 40x = 0
40x + 52x2 + -12x3 = 0 + -52x2 + 52x2 + 12x3 + -12x3
40x + 52x2 + -12x3 = -52x2 + 52x2 + 12x3 + -12x3

Combine like terms: -52x2 + 52x2 = 0
40x + 52x2 + -12x3 = 0 + 12x3 + -12x3
40x + 52x2 + -12x3 = 12x3 + -12x3

Combine like terms: 12x3 + -12x3 = 0
40x + 52x2 + -12x3 = 0

Factor out the Greatest Common Factor (GCF), '4x'.
4x(10 + 13x + -3x2) = 0

Factor a trinomial.
4x((5 + -1x)(2 + 3x)) = 0

Ignore the factor 4.

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

Subproblem 3

Set the factor '(2 + 3x)' equal to zero and attempt to solve: Simplifying 2 + 3x = 0 Solving 2 + 3x = 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 + 3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3x = 0 + -2 3x = 0 + -2 Combine like terms: 0 + -2 = -2 3x = -2 Divide each side by '3'. x = -0.6666666667 Simplifying x = -0.6666666667

Solution

x = {0, 5, -0.6666666667}

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