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

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


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

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

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

Multiply (-9 + 4x) * (-9 + 4x)
5x(-9(-9 + 4x) + 4x * (-9 + 4x)) = 0
5x((-9 * -9 + 4x * -9) + 4x * (-9 + 4x)) = 0
5x((81 + -36x) + 4x * (-9 + 4x)) = 0
5x(81 + -36x + (-9 * 4x + 4x * 4x)) = 0
5x(81 + -36x + (-36x + 16x2)) = 0

Combine like terms: -36x + -36x = -72x
5x(81 + -72x + 16x2) = 0
(81 * 5x + -72x * 5x + 16x2 * 5x) = 0
(405x + -360x2 + 80x3) = 0

Solving
405x + -360x2 + 80x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5x'.
5x(81 + -72x + 16x2) = 0

Factor a trinomial.
5x((9 + -4x)(9 + -4x)) = 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 '(9 + -4x)' equal to zero and attempt to solve:

Simplifying
9 + -4x = 0

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

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

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

Divide each side by '-4'.
x = 2.25

Simplifying
x = 2.25

Subproblem 3
Set the factor '(9 + -4x)' equal to zero and attempt to solve:

Simplifying
9 + -4x = 0

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

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

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

Divide each side by '-4'.
x = 2.25

Simplifying
x = 2.25
Solution
x = {0, 2.25, 2.25}

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