x^2(x-9)(2x+1)=0

Solution for x^2(x-9)(2x+1)=0 equation:

Simplifying
x2(x + -9)(2x + 1) = 0

Reorder the terms:
x2(-9 + x)(2x + 1) = 0

Reorder the terms:
x2(-9 + x)(1 + 2x) = 0

Multiply (-9 + x) * (1 + 2x)
x2(-9(1 + 2x) + x(1 + 2x)) = 0
x2((1 * -9 + 2x * -9) + x(1 + 2x)) = 0
x2((-9 + -18x) + x(1 + 2x)) = 0
x2(-9 + -18x + (1 * x + 2x * x)) = 0
x2(-9 + -18x + (1x + 2x2)) = 0

Combine like terms: -18x + 1x = -17x
x2(-9 + -17x + 2x2) = 0
(-9 * x2 + -17x * x2 + 2x2 * x2) = 0
(-9x2 + -17x3 + 2x4) = 0

Solving
-9x2 + -17x3 + 2x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-9 + -17x + 2x2) = 0

Factor a trinomial.
x2((-1 + -2x)(9 + -1x)) = 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 + -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 '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 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 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {0, -0.5, 9}