10x^3+20x^2=-6x^3+6x

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Solution for 10x^3+20x^2=-6x^3+6x equation:


Simplifying
10x3 + 20x2 = -6x3 + 6x

Reorder the terms:
20x2 + 10x3 = -6x3 + 6x

Reorder the terms:
20x2 + 10x3 = 6x + -6x3

Solving
20x2 + 10x3 = 6x + -6x3

Solving for variable 'x'.

Reorder the terms:
-6x + 20x2 + 10x3 + 6x3 = 6x + -6x3 + -6x + 6x3

Combine like terms: 10x3 + 6x3 = 16x3
-6x + 20x2 + 16x3 = 6x + -6x3 + -6x + 6x3

Reorder the terms:
-6x + 20x2 + 16x3 = 6x + -6x + -6x3 + 6x3

Combine like terms: 6x + -6x = 0
-6x + 20x2 + 16x3 = 0 + -6x3 + 6x3
-6x + 20x2 + 16x3 = -6x3 + 6x3

Combine like terms: -6x3 + 6x3 = 0
-6x + 20x2 + 16x3 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-3 + 10x + 8x2) = 0

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

Ignore the factor 2.

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 '(-3 + -2x)' equal to zero and attempt to solve: Simplifying -3 + -2x = 0 Solving -3 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2x = 0 + 3 -2x = 0 + 3 Combine like terms: 0 + 3 = 3 -2x = 3 Divide each side by '-2'. x = -1.5 Simplifying x = -1.5

Subproblem 3

Set the factor '(1 + -4x)' equal to zero and attempt to solve: Simplifying 1 + -4x = 0 Solving 1 + -4x = 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 + -4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4x = 0 + -1 -4x = 0 + -1 Combine like terms: 0 + -1 = -1 -4x = -1 Divide each side by '-4'. x = 0.25 Simplifying x = 0.25

Solution

x = {0, -1.5, 0.25}

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