-9x^4+24x^3-16x^2=0

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Solution for -9x^4+24x^3-16x^2=0 equation: 


Simplifying
-9x4 + 24x3 + -16x2 = 0

Reorder the terms:
-16x2 + 24x3 + -9x4 = 0

Solving
-16x2 + 24x3 + -9x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-16 + 24x + -9x2) = 0

Factor a trinomial.
x2((-4 + 3x)(4 + -3x)) = 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 '(-4 + 3x)' equal to zero and attempt to solve:

Simplifying
-4 + 3x = 0

Solving
-4 + 3x = 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 + 3x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 3x = 0 + 4
3x = 0 + 4

Combine like terms: 0 + 4 = 4
3x = 4

Divide each side by '3'.
x = 1.333333333

Simplifying
x = 1.333333333

Subproblem 3
Set the factor '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 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 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333
Solution
x = {0, 1.333333333, 1.333333333}

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