-6x^3+75x^2-126x=0

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Solution for -6x^3+75x^2-126x=0 equation:


Simplifying
-6x3 + 75x2 + -126x = 0

Reorder the terms:
-126x + 75x2 + -6x3 = 0

Solving
-126x + 75x2 + -6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-42 + 25x + -2x2) = 0

Factor a trinomial.
3x((-21 + 2x)(2 + -1x)) = 0

Ignore the factor 3.

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 '(-21 + 2x)' equal to zero and attempt to solve: Simplifying -21 + 2x = 0 Solving -21 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + 2x = 0 + 21 Combine like terms: -21 + 21 = 0 0 + 2x = 0 + 21 2x = 0 + 21 Combine like terms: 0 + 21 = 21 2x = 21 Divide each side by '2'. x = 10.5 Simplifying x = 10.5

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, 10.5, 2}

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