9x(2x-1)(5x-2)=0

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Solution for 9x(2x-1)(5x-2)=0 equation: 


Simplifying
9x(2x + -1)(5x + -2) = 0

Reorder the terms:
9x(-1 + 2x)(5x + -2) = 0

Reorder the terms:
9x(-1 + 2x)(-2 + 5x) = 0

Multiply (-1 + 2x) * (-2 + 5x)
9x(-1(-2 + 5x) + 2x * (-2 + 5x)) = 0
9x((-2 * -1 + 5x * -1) + 2x * (-2 + 5x)) = 0
9x((2 + -5x) + 2x * (-2 + 5x)) = 0
9x(2 + -5x + (-2 * 2x + 5x * 2x)) = 0
9x(2 + -5x + (-4x + 10x2)) = 0

Combine like terms: -5x + -4x = -9x
9x(2 + -9x + 10x2) = 0
(2 * 9x + -9x * 9x + 10x2 * 9x) = 0
(18x + -81x2 + 90x3) = 0

Solving
18x + -81x2 + 90x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '9x'.
9x(2 + -9x + 10x2) = 0

Factor a trinomial.
9x((2 + -5x)(1 + -2x)) = 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 '(2 + -5x)' equal to zero and attempt to solve:

Simplifying
2 + -5x = 0

Solving
2 + -5x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -5x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5x = 0 + -2
-5x = 0 + -2

Combine like terms: 0 + -2 = -2
-5x = -2

Divide each side by '-5'.
x = 0.4

Simplifying
x = 0.4

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, 0.4, 0.5}

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