4x(3x-1)(4x+9)=0

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Solution for 4x(3x-1)(4x+9)=0 equation: 


Simplifying
4x(3x + -1)(4x + 9) = 0

Reorder the terms:
4x(-1 + 3x)(4x + 9) = 0

Reorder the terms:
4x(-1 + 3x)(9 + 4x) = 0

Multiply (-1 + 3x) * (9 + 4x)
4x(-1(9 + 4x) + 3x * (9 + 4x)) = 0
4x((9 * -1 + 4x * -1) + 3x * (9 + 4x)) = 0
4x((-9 + -4x) + 3x * (9 + 4x)) = 0
4x(-9 + -4x + (9 * 3x + 4x * 3x)) = 0
4x(-9 + -4x + (27x + 12x2)) = 0

Combine like terms: -4x + 27x = 23x
4x(-9 + 23x + 12x2) = 0
(-9 * 4x + 23x * 4x + 12x2 * 4x) = 0
(-36x + 92x2 + 48x3) = 0

Solving
-36x + 92x2 + 48x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(-9 + 23x + 12x2) = 0

Factor a trinomial.
4x((-9 + -4x)(1 + -3x)) = 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 '(-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 '(1 + -3x)' equal to zero and attempt to solve:

Simplifying
1 + -3x = 0

Solving
1 + -3x = 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 + -3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3x = 0 + -1
-3x = 0 + -1

Combine like terms: 0 + -1 = -1
-3x = -1

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Solution
x = {0, -2.25, 0.3333333333}

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