6x^3+8x^2-63x=2x^2+9x

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Solution for 6x^3+8x^2-63x=2x^2+9x equation:


Simplifying
6x3 + 8x2 + -63x = 2x2 + 9x

Reorder the terms:
-63x + 8x2 + 6x3 = 2x2 + 9x

Reorder the terms:
-63x + 8x2 + 6x3 = 9x + 2x2

Solving
-63x + 8x2 + 6x3 = 9x + 2x2

Solving for variable 'x'.

Reorder the terms:
-63x + -9x + 8x2 + -2x2 + 6x3 = 9x + 2x2 + -9x + -2x2

Combine like terms: -63x + -9x = -72x
-72x + 8x2 + -2x2 + 6x3 = 9x + 2x2 + -9x + -2x2

Combine like terms: 8x2 + -2x2 = 6x2
-72x + 6x2 + 6x3 = 9x + 2x2 + -9x + -2x2

Reorder the terms:
-72x + 6x2 + 6x3 = 9x + -9x + 2x2 + -2x2

Combine like terms: 9x + -9x = 0
-72x + 6x2 + 6x3 = 0 + 2x2 + -2x2
-72x + 6x2 + 6x3 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-72x + 6x2 + 6x3 = 0

Factor out the Greatest Common Factor (GCF), '6x'.
6x(-12 + x + x2) = 0

Factor a trinomial.
6x((-4 + -1x)(3 + -1x)) = 0

Ignore the factor 6.

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 '(-4 + -1x)' equal to zero and attempt to solve: Simplifying -4 + -1x = 0 Solving -4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1x = 0 + 4 -1x = 0 + 4 Combine like terms: 0 + 4 = 4 -1x = 4 Divide each side by '-1'. x = -4 Simplifying x = -4

Subproblem 3

Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3

Solution

x = {0, -4, 3}

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