x^4-12x^2=x^3

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Solution for x^4-12x^2=x^3 equation:


Simplifying
x4 + -12x2 = x3

Reorder the terms:
-12x2 + x4 = x3

Solving
-12x2 + x4 = x3

Solving for variable 'x'.

Reorder the terms:
-12x2 + -1x3 + x4 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
-12x2 + -1x3 + x4 = 0

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-12 + -1x + x2) = 0

Factor a trinomial.
x2((-3 + -1x)(4 + -1x)) = 0

Subproblem 1

Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}

Subproblem 2

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

Subproblem 3

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

Solution

x = {0, -3, 4}

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