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

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


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

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

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

Multiply (-9 + 4x) * (8 + 9x)
4x(-9(8 + 9x) + 4x * (8 + 9x)) = 0
4x((8 * -9 + 9x * -9) + 4x * (8 + 9x)) = 0
4x((-72 + -81x) + 4x * (8 + 9x)) = 0
4x(-72 + -81x + (8 * 4x + 9x * 4x)) = 0
4x(-72 + -81x + (32x + 36x2)) = 0

Combine like terms: -81x + 32x = -49x
4x(-72 + -49x + 36x2) = 0
(-72 * 4x + -49x * 4x + 36x2 * 4x) = 0
(-288x + -196x2 + 144x3) = 0

Solving
-288x + -196x2 + 144x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(-72 + -49x + 36x2) = 0

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

Ignore the factor 4.

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 '(-8 + -9x)' equal to zero and attempt to solve:

Simplifying
-8 + -9x = 0

Solving
-8 + -9x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -9x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -9x = 0 + 8
-9x = 0 + 8

Combine like terms: 0 + 8 = 8
-9x = 8

Divide each side by '-9'.
x = -0.8888888889

Simplifying
x = -0.8888888889

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, -0.8888888889, 2.25}

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