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

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


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

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

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

Multiply (4 + x) * (-9 + 4x)
2x(4(-9 + 4x) + x(-9 + 4x)) = 0
2x((-9 * 4 + 4x * 4) + x(-9 + 4x)) = 0
2x((-36 + 16x) + x(-9 + 4x)) = 0
2x(-36 + 16x + (-9 * x + 4x * x)) = 0
2x(-36 + 16x + (-9x + 4x2)) = 0

Combine like terms: 16x + -9x = 7x
2x(-36 + 7x + 4x2) = 0
(-36 * 2x + 7x * 2x + 4x2 * 2x) = 0
(-72x + 14x2 + 8x3) = 0

Solving
-72x + 14x2 + 8x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-36 + 7x + 4x2) = 0

Factor a trinomial.
2x((-4 + -1x)(9 + -4x)) = 0

Ignore the factor 2.

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

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

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

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

Divide each side by '-1'.
x = -4

Simplifying
x = -4

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, -4, 2.25}

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