x(4x+1)(5x-9)=0

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Solution for x(4x+1)(5x-9)=0 equation: 


Simplifying
x(4x + 1)(5x + -9) = 0

Reorder the terms:
x(1 + 4x)(5x + -9) = 0

Reorder the terms:
x(1 + 4x)(-9 + 5x) = 0

Multiply (1 + 4x) * (-9 + 5x)
x(1(-9 + 5x) + 4x * (-9 + 5x)) = 0
x((-9 * 1 + 5x * 1) + 4x * (-9 + 5x)) = 0
x((-9 + 5x) + 4x * (-9 + 5x)) = 0
x(-9 + 5x + (-9 * 4x + 5x * 4x)) = 0
x(-9 + 5x + (-36x + 20x2)) = 0

Combine like terms: 5x + -36x = -31x
x(-9 + -31x + 20x2) = 0
(-9 * x + -31x * x + 20x2 * x) = 0
(-9x + -31x2 + 20x3) = 0

Solving
-9x + -31x2 + 20x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-9 + -31x + 20x2) = 0

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


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 '(-1 + -4x)' equal to zero and attempt to solve:

Simplifying
-1 + -4x = 0

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

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

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

Divide each side by '-4'.
x = -0.25

Simplifying
x = -0.25

Subproblem 3
Set the factor '(9 + -5x)' equal to zero and attempt to solve:

Simplifying
9 + -5x = 0

Solving
9 + -5x = 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 + -5x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -5x = 0 + -9
-5x = 0 + -9

Combine like terms: 0 + -9 = -9
-5x = -9

Divide each side by '-5'.
x = 1.8

Simplifying
x = 1.8
Solution
x = {0, -0.25, 1.8}

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