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

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


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

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

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

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

Multiply (4 + x) * (-6 + x)
0 = x(4(-6 + x) + x(-6 + x))(7 + x)
0 = x((-6 * 4 + x * 4) + x(-6 + x))(7 + x)
0 = x((-24 + 4x) + x(-6 + x))(7 + x)
0 = x(-24 + 4x + (-6 * x + x * x))(7 + x)
0 = x(-24 + 4x + (-6x + x2))(7 + x)

Combine like terms: 4x + -6x = -2x
0 = x(-24 + -2x + x2)(7 + x)

Multiply (-24 + -2x + x2) * (7 + x)
0 = x(-24(7 + x) + -2x * (7 + x) + x2(7 + x))
0 = x((7 * -24 + x * -24) + -2x * (7 + x) + x2(7 + x))
0 = x((-168 + -24x) + -2x * (7 + x) + x2(7 + x))
0 = x(-168 + -24x + (7 * -2x + x * -2x) + x2(7 + x))
0 = x(-168 + -24x + (-14x + -2x2) + x2(7 + x))
0 = x(-168 + -24x + -14x + -2x2 + (7 * x2 + x * x2))
0 = x(-168 + -24x + -14x + -2x2 + (7x2 + x3))

Combine like terms: -24x + -14x = -38x
0 = x(-168 + -38x + -2x2 + 7x2 + x3)

Combine like terms: -2x2 + 7x2 = 5x2
0 = x(-168 + -38x + 5x2 + x3)
0 = (-168 * x + -38x * x + 5x2 * x + x3 * x)
0 = (-168x + -38x2 + 5x3 + x4)

Solving
0 = -168x + -38x2 + 5x3 + x4

Solving for variable 'x'.
Remove the zero:
168x + 38x2 + -5x3 + -1x4 = -168x + -38x2 + 5x3 + x4 + 168x + 38x2 + -5x3 + -1x4

Reorder the terms:
168x + 38x2 + -5x3 + -1x4 = -168x + 168x + -38x2 + 38x2 + 5x3 + -5x3 + x4 + -1x4

Combine like terms: -168x + 168x = 0
168x + 38x2 + -5x3 + -1x4 = 0 + -38x2 + 38x2 + 5x3 + -5x3 + x4 + -1x4
168x + 38x2 + -5x3 + -1x4 = -38x2 + 38x2 + 5x3 + -5x3 + x4 + -1x4

Combine like terms: -38x2 + 38x2 = 0
168x + 38x2 + -5x3 + -1x4 = 0 + 5x3 + -5x3 + x4 + -1x4
168x + 38x2 + -5x3 + -1x4 = 5x3 + -5x3 + x4 + -1x4

Combine like terms: 5x3 + -5x3 = 0
168x + 38x2 + -5x3 + -1x4 = 0 + x4 + -1x4
168x + 38x2 + -5x3 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
168x + 38x2 + -5x3 + -1x4 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(168 + 38x + -5x2 + -1x3) = 0


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 '(168 + 38x + -5x2 + -1x3)' equal to zero and attempt to solve:

Simplifying
168 + 38x + -5x2 + -1x3 = 0

Solving
168 + 38x + -5x2 + -1x3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}

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