4x(2x+9)(x-3)=0

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Solution for 4x(2x+9)(x-3)=0 equation: 


Simplifying
4x(2x + 9)(x + -3) = 0

Reorder the terms:
4x(9 + 2x)(x + -3) = 0

Reorder the terms:
4x(9 + 2x)(-3 + x) = 0

Multiply (9 + 2x) * (-3 + x)
4x(9(-3 + x) + 2x * (-3 + x)) = 0
4x((-3 * 9 + x * 9) + 2x * (-3 + x)) = 0
4x((-27 + 9x) + 2x * (-3 + x)) = 0
4x(-27 + 9x + (-3 * 2x + x * 2x)) = 0
4x(-27 + 9x + (-6x + 2x2)) = 0

Combine like terms: 9x + -6x = 3x
4x(-27 + 3x + 2x2) = 0
(-27 * 4x + 3x * 4x + 2x2 * 4x) = 0
(-108x + 12x2 + 8x3) = 0

Solving
-108x + 12x2 + 8x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(-27 + 3x + 2x2) = 0

Factor a trinomial.
4x((-9 + -2x)(3 + -1x)) = 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 + -2x)' equal to zero and attempt to solve:

Simplifying
-9 + -2x = 0

Solving
-9 + -2x = 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 + -2x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2x = 0 + 9
-2x = 0 + 9

Combine like terms: 0 + 9 = 9
-2x = 9

Divide each side by '-2'.
x = -4.5

Simplifying
x = -4.5

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

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

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

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

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {0, -4.5, 3}

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