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

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


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

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

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

Multiply (7 + x) * (-4 + 3x)
3x(7(-4 + 3x) + x(-4 + 3x)) = 0
3x((-4 * 7 + 3x * 7) + x(-4 + 3x)) = 0
3x((-28 + 21x) + x(-4 + 3x)) = 0
3x(-28 + 21x + (-4 * x + 3x * x)) = 0
3x(-28 + 21x + (-4x + 3x2)) = 0

Combine like terms: 21x + -4x = 17x
3x(-28 + 17x + 3x2) = 0
(-28 * 3x + 17x * 3x + 3x2 * 3x) = 0
(-84x + 51x2 + 9x3) = 0

Solving
-84x + 51x2 + 9x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-28 + 17x + 3x2) = 0

Factor a trinomial.
3x((-7 + -1x)(4 + -3x)) = 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 '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 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 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7

Subproblem 3
Set the factor '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 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 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333
Solution
x = {0, -7, 1.333333333}

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