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

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


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

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

Multiply (1 + -4x) * (4 + 7x)
-3x(1(4 + 7x) + -4x * (4 + 7x)) = 0
-3x((4 * 1 + 7x * 1) + -4x * (4 + 7x)) = 0
-3x((4 + 7x) + -4x * (4 + 7x)) = 0
-3x(4 + 7x + (4 * -4x + 7x * -4x)) = 0
-3x(4 + 7x + (-16x + -28x2)) = 0

Combine like terms: 7x + -16x = -9x
-3x(4 + -9x + -28x2) = 0
(4 * -3x + -9x * -3x + -28x2 * -3x) = 0
(-12x + 27x2 + 84x3) = 0

Solving
-12x + 27x2 + 84x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-4 + 9x + 28x2) = 0

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

Subproblem 3
Set the factor '(1 + -4x)' equal to zero and attempt to solve:

Simplifying
1 + -4x = 0

Solving
1 + -4x = 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 + -4x = 0 + -1

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

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

Divide each side by '-4'.
x = 0.25

Simplifying
x = 0.25
Solution
x = {0, -0.5714285714, 0.25}

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