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

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


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

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

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

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

Combine like terms: -1x + 21x = 20x
4x(-7 + 20x + 3x2) = 0
(-7 * 4x + 20x * 4x + 3x2 * 4x) = 0
(-28x + 80x2 + 12x3) = 0

Solving
-28x + 80x2 + 12x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(-7 + 20x + 3x2) = 0

Factor a trinomial.
4x((-7 + -1x)(1 + -3x)) = 0

Ignore the factor 4.

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 '(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
Solution
x = {0, -7, 0.3333333333}

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