0=30x^4+3x^3-9x^2

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Solution for 0=30x^4+3x^3-9x^2 equation:


Simplifying
0 = 30x4 + 3x3 + -9x2

Reorder the terms:
0 = -9x2 + 3x3 + 30x4

Solving
0 = -9x2 + 3x3 + 30x4

Solving for variable 'x'.
Remove the zero:
9x2 + -3x3 + -30x4 = -9x2 + 3x3 + 30x4 + 9x2 + -3x3 + -30x4

Reorder the terms:
9x2 + -3x3 + -30x4 = -9x2 + 9x2 + 3x3 + -3x3 + 30x4 + -30x4

Combine like terms: -9x2 + 9x2 = 0
9x2 + -3x3 + -30x4 = 0 + 3x3 + -3x3 + 30x4 + -30x4
9x2 + -3x3 + -30x4 = 3x3 + -3x3 + 30x4 + -30x4

Combine like terms: 3x3 + -3x3 = 0
9x2 + -3x3 + -30x4 = 0 + 30x4 + -30x4
9x2 + -3x3 + -30x4 = 30x4 + -30x4

Combine like terms: 30x4 + -30x4 = 0
9x2 + -3x3 + -30x4 = 0

Factor out the Greatest Common Factor (GCF), '3x2'.
3x2(3 + -1x + -10x2) = 0

Factor a trinomial.
3x2((1 + -2x)(3 + 5x)) = 0

Ignore the factor 3.

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 '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 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 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5

Subproblem 3

Set the factor '(3 + 5x)' equal to zero and attempt to solve: Simplifying 3 + 5x = 0 Solving 3 + 5x = 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 + 5x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 5x = 0 + -3 5x = 0 + -3 Combine like terms: 0 + -3 = -3 5x = -3 Divide each side by '5'. x = -0.6 Simplifying x = -0.6

Solution

x = {0, 0.5, -0.6}

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