0=x^4+8x^3-9x^2

Solution for 0=x^4+8x^3-9x^2 equation:

Simplifying
0 = x4 + 8x3 + -9x2

Reorder the terms:
0 = -9x2 + 8x3 + x4

Solving
0 = -9x2 + 8x3 + x4

Solving for variable 'x'.
Remove the zero:
9x2 + -8x3 + -1x4 = -9x2 + 8x3 + x4 + 9x2 + -8x3 + -1x4

Reorder the terms:
9x2 + -8x3 + -1x4 = -9x2 + 9x2 + 8x3 + -8x3 + x4 + -1x4

Combine like terms: -9x2 + 9x2 = 0
9x2 + -8x3 + -1x4 = 0 + 8x3 + -8x3 + x4 + -1x4
9x2 + -8x3 + -1x4 = 8x3 + -8x3 + x4 + -1x4

Combine like terms: 8x3 + -8x3 = 0
9x2 + -8x3 + -1x4 = 0 + x4 + -1x4
9x2 + -8x3 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
9x2 + -8x3 + -1x4 = 0

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(9 + -8x + -1x2) = 0

Factor a trinomial.
x2((1 + -1x)(9 + x)) = 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 '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 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 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Subproblem 3
Set the factor '(9 + x)' equal to zero and attempt to solve:

Simplifying
9 + x = 0

Solving
9 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-9' to each side of the equation.
9 + -9 + x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + x = 0 + -9
x = 0 + -9

Combine like terms: 0 + -9 = -9
x = -9

Simplifying
x = -9
Solution
x = {0, 1, -9}