3x(2x-7)(4x+9)=0

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Solution for 3x(2x-7)(4x+9)=0 equation: 


Simplifying
3x(2x + -7)(4x + 9) = 0

Reorder the terms:
3x(-7 + 2x)(4x + 9) = 0

Reorder the terms:
3x(-7 + 2x)(9 + 4x) = 0

Multiply (-7 + 2x) * (9 + 4x)
3x(-7(9 + 4x) + 2x * (9 + 4x)) = 0
3x((9 * -7 + 4x * -7) + 2x * (9 + 4x)) = 0
3x((-63 + -28x) + 2x * (9 + 4x)) = 0
3x(-63 + -28x + (9 * 2x + 4x * 2x)) = 0
3x(-63 + -28x + (18x + 8x2)) = 0

Combine like terms: -28x + 18x = -10x
3x(-63 + -10x + 8x2) = 0
(-63 * 3x + -10x * 3x + 8x2 * 3x) = 0
(-189x + -30x2 + 24x3) = 0

Solving
-189x + -30x2 + 24x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-63 + -10x + 8x2) = 0

Factor a trinomial.
3x((-9 + -4x)(7 + -2x)) = 0

Ignore the factor 3.

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 '(7 + -2x)' equal to zero and attempt to solve:

Simplifying
7 + -2x = 0

Solving
7 + -2x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x = 0 + -7
-2x = 0 + -7

Combine like terms: 0 + -7 = -7
-2x = -7

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5
Solution
x = {0, -2.25, 3.5}

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