15x^3+9x^2=6x^4

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Solution for 15x^3+9x^2=6x^4 equation:


Simplifying
15x3 + 9x2 = 6x4

Reorder the terms:
9x2 + 15x3 = 6x4

Solving
9x2 + 15x3 = 6x4

Solving for variable 'x'.

Combine like terms: 6x4 + -6x4 = 0
9x2 + 15x3 + -6x4 = 0

Factor out the Greatest Common Factor (GCF), '3x2'.
3x2(3 + 5x + -2x2) = 0

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

Solution

x = {0, 3, -0.5}

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