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

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


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

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

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

Multiply (-4 + 9x) * (-5 + x)
5x(-4(-5 + x) + 9x * (-5 + x)) = 0
5x((-5 * -4 + x * -4) + 9x * (-5 + x)) = 0
5x((20 + -4x) + 9x * (-5 + x)) = 0
5x(20 + -4x + (-5 * 9x + x * 9x)) = 0
5x(20 + -4x + (-45x + 9x2)) = 0

Combine like terms: -4x + -45x = -49x
5x(20 + -49x + 9x2) = 0
(20 * 5x + -49x * 5x + 9x2 * 5x) = 0
(100x + -245x2 + 45x3) = 0

Solving
100x + -245x2 + 45x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5x'.
5x(20 + -49x + 9x2) = 0

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

Ignore the factor 5.

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 '(4 + -9x)' equal to zero and attempt to solve:

Simplifying
4 + -9x = 0

Solving
4 + -9x = 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 + -9x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -9x = 0 + -4
-9x = 0 + -4

Combine like terms: 0 + -4 = -4
-9x = -4

Divide each side by '-9'.
x = 0.4444444444

Simplifying
x = 0.4444444444

Subproblem 3
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {0, 0.4444444444, 5}

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