12x^3=35x-16x^2

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Solution for 12x^3=35x-16x^2 equation:


Simplifying
12x3 = 35x + -16x2

Solving
12x3 = 35x + -16x2

Solving for variable 'x'.

Reorder the terms:
-35x + 16x2 + 12x3 = 35x + -16x2 + -35x + 16x2

Reorder the terms:
-35x + 16x2 + 12x3 = 35x + -35x + -16x2 + 16x2

Combine like terms: 35x + -35x = 0
-35x + 16x2 + 12x3 = 0 + -16x2 + 16x2
-35x + 16x2 + 12x3 = -16x2 + 16x2

Combine like terms: -16x2 + 16x2 = 0
-35x + 16x2 + 12x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-35 + 16x + 12x2) = 0

Factor a trinomial.
x((-5 + -2x)(7 + -6x)) = 0

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 + -2x)' equal to zero and attempt to solve: Simplifying -5 + -2x = 0 Solving -5 + -2x = 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 + -2x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2x = 0 + 5 -2x = 0 + 5 Combine like terms: 0 + 5 = 5 -2x = 5 Divide each side by '-2'. x = -2.5 Simplifying x = -2.5

Subproblem 3

Set the factor '(7 + -6x)' equal to zero and attempt to solve: Simplifying 7 + -6x = 0 Solving 7 + -6x = 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 + -6x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -6x = 0 + -7 -6x = 0 + -7 Combine like terms: 0 + -7 = -7 -6x = -7 Divide each side by '-6'. x = 1.166666667 Simplifying x = 1.166666667

Solution

x = {0, -2.5, 1.166666667}

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