4x(x+6)(x-7)=0

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Solution for 4x(x+6)(x-7)=0 equation: 


Simplifying
4x(x + 6)(x + -7) = 0

Reorder the terms:
4x(6 + x)(x + -7) = 0

Reorder the terms:
4x(6 + x)(-7 + x) = 0

Multiply (6 + x) * (-7 + x)
4x(6(-7 + x) + x(-7 + x)) = 0
4x((-7 * 6 + x * 6) + x(-7 + x)) = 0
4x((-42 + 6x) + x(-7 + x)) = 0
4x(-42 + 6x + (-7 * x + x * x)) = 0
4x(-42 + 6x + (-7x + x2)) = 0

Combine like terms: 6x + -7x = -1x
4x(-42 + -1x + x2) = 0
(-42 * 4x + -1x * 4x + x2 * 4x) = 0
(-168x + -4x2 + 4x3) = 0

Solving
-168x + -4x2 + 4x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(-42 + -1x + x2) = 0

Factor a trinomial.
4x((-6 + -1x)(7 + -1x)) = 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 '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6

Subproblem 3
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
Solution
x = {0, -6, 7}

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