-2x(3x-1)(7x+4)=0

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Solution for -2x(3x-1)(7x+4)=0 equation: 


Simplifying
-2x(3x + -1)(7x + 4) = 0

Reorder the terms:
-2x(-1 + 3x)(7x + 4) = 0

Reorder the terms:
-2x(-1 + 3x)(4 + 7x) = 0

Multiply (-1 + 3x) * (4 + 7x)
-2x(-1(4 + 7x) + 3x * (4 + 7x)) = 0
-2x((4 * -1 + 7x * -1) + 3x * (4 + 7x)) = 0
-2x((-4 + -7x) + 3x * (4 + 7x)) = 0
-2x(-4 + -7x + (4 * 3x + 7x * 3x)) = 0
-2x(-4 + -7x + (12x + 21x2)) = 0

Combine like terms: -7x + 12x = 5x
-2x(-4 + 5x + 21x2) = 0
(-4 * -2x + 5x * -2x + 21x2 * -2x) = 0
(8x + -10x2 + -42x3) = 0

Solving
8x + -10x2 + -42x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(4 + -5x + -21x2) = 0

Factor a trinomial.
2x((1 + -3x)(4 + 7x)) = 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 '(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

Subproblem 3
Set the factor '(4 + 7x)' equal to zero and attempt to solve:

Simplifying
4 + 7x = 0

Solving
4 + 7x = 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 + 7x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 7x = 0 + -4
7x = 0 + -4

Combine like terms: 0 + -4 = -4
7x = -4

Divide each side by '7'.
x = -0.5714285714

Simplifying
x = -0.5714285714
Solution
x = {0, 0.3333333333, -0.5714285714}

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