(9x(x-4)(8x-5))=0

Solution for (9x(x-4)(8x-5))=0 equation:

Simplifying
(9x(x + -4)(8x + -5)) = 0

Reorder the terms:
(9x(-4 + x)(8x + -5)) = 0

Reorder the terms:
(9x(-4 + x)(-5 + 8x)) = 0

Multiply (-4 + x) * (-5 + 8x)
(9x(-4(-5 + 8x) + x(-5 + 8x))) = 0
(9x((-5 * -4 + 8x * -4) + x(-5 + 8x))) = 0
(9x((20 + -32x) + x(-5 + 8x))) = 0
(9x(20 + -32x + (-5 * x + 8x * x))) = 0
(9x(20 + -32x + (-5x + 8x2))) = 0

Combine like terms: -32x + -5x = -37x
(9x(20 + -37x + 8x2)) = 0
((20 * 9x + -37x * 9x + 8x2 * 9x)) = 0
((180x + -333x2 + 72x3)) = 0
(180x + -333x2 + 72x3) = 0

Remove parenthesis around (180x + -333x2 + 72x3)
180x + -333x2 + 72x3 = 0

Solving
180x + -333x2 + 72x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '9x'.
9x(20 + -37x + 8x2) = 0

Factor a trinomial.
9x((5 + -8x)(4 + -1x)) = 0

Ignore the factor 9.
Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(5 + -8x)' equal to zero and attempt to solve:

Simplifying
5 + -8x = 0

Solving
5 + -8x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -8x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -8x = 0 + -5
-8x = 0 + -5

Combine like terms: 0 + -5 = -5
-8x = -5

Divide each side by '-8'.
x = 0.625

Simplifying
x = 0.625
Subproblem 3
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {0, 0.625, 4}