72x^4+78x^3-330x^2=0

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Solution for 72x^4+78x^3-330x^2=0 equation:


Simplifying
72x4 + 78x3 + -330x2 = 0

Reorder the terms:
-330x2 + 78x3 + 72x4 = 0

Solving
-330x2 + 78x3 + 72x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6x2'.
6x2(-55 + 13x + 12x2) = 0

Factor a trinomial.
6x2((-11 + -4x)(5 + -3x)) = 0

Ignore the factor 6.

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 '(-11 + -4x)' equal to zero and attempt to solve: Simplifying -11 + -4x = 0 Solving -11 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + -4x = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -4x = 0 + 11 -4x = 0 + 11 Combine like terms: 0 + 11 = 11 -4x = 11 Divide each side by '-4'. x = -2.75 Simplifying x = -2.75

Subproblem 3

Set the factor '(5 + -3x)' equal to zero and attempt to solve: Simplifying 5 + -3x = 0 Solving 5 + -3x = 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 + -3x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3x = 0 + -5 -3x = 0 + -5 Combine like terms: 0 + -5 = -5 -3x = -5 Divide each side by '-3'. x = 1.666666667 Simplifying x = 1.666666667

Solution

x = {0, -2.75, 1.666666667}

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