4x^4+24x^3+32x^2=0

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Solution for 4x^4+24x^3+32x^2=0 equation:


Simplifying
4x4 + 24x3 + 32x2 = 0

Reorder the terms:
32x2 + 24x3 + 4x4 = 0

Solving
32x2 + 24x3 + 4x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x2'.
4x2(8 + 6x + x2) = 0

Factor a trinomial.
4x2((4 + x)(2 + x)) = 0

Ignore the factor 4.

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 '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 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 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4

Subproblem 3

Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2

Solution

x = {0, -4, -2}

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