0=x(3x-7)(4x+2)(6x-13)

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Solution for 0=x(3x-7)(4x+2)(6x-13) equation: 


Simplifying
0 = x(3x + -7)(4x + 2)(6x + -13)

Reorder the terms:
0 = x(-7 + 3x)(4x + 2)(6x + -13)

Reorder the terms:
0 = x(-7 + 3x)(2 + 4x)(6x + -13)

Reorder the terms:
0 = x(-7 + 3x)(2 + 4x)(-13 + 6x)

Multiply (-7 + 3x) * (2 + 4x)
0 = x(-7(2 + 4x) + 3x * (2 + 4x))(-13 + 6x)
0 = x((2 * -7 + 4x * -7) + 3x * (2 + 4x))(-13 + 6x)
0 = x((-14 + -28x) + 3x * (2 + 4x))(-13 + 6x)
0 = x(-14 + -28x + (2 * 3x + 4x * 3x))(-13 + 6x)
0 = x(-14 + -28x + (6x + 12x2))(-13 + 6x)

Combine like terms: -28x + 6x = -22x
0 = x(-14 + -22x + 12x2)(-13 + 6x)

Multiply (-14 + -22x + 12x2) * (-13 + 6x)
0 = x(-14(-13 + 6x) + -22x * (-13 + 6x) + 12x2 * (-13 + 6x))
0 = x((-13 * -14 + 6x * -14) + -22x * (-13 + 6x) + 12x2 * (-13 + 6x))
0 = x((182 + -84x) + -22x * (-13 + 6x) + 12x2 * (-13 + 6x))
0 = x(182 + -84x + (-13 * -22x + 6x * -22x) + 12x2 * (-13 + 6x))
0 = x(182 + -84x + (286x + -132x2) + 12x2 * (-13 + 6x))
0 = x(182 + -84x + 286x + -132x2 + (-13 * 12x2 + 6x * 12x2))
0 = x(182 + -84x + 286x + -132x2 + (-156x2 + 72x3))

Combine like terms: -84x + 286x = 202x
0 = x(182 + 202x + -132x2 + -156x2 + 72x3)

Combine like terms: -132x2 + -156x2 = -288x2
0 = x(182 + 202x + -288x2 + 72x3)
0 = (182 * x + 202x * x + -288x2 * x + 72x3 * x)
0 = (182x + 202x2 + -288x3 + 72x4)

Solving
0 = 182x + 202x2 + -288x3 + 72x4

Solving for variable 'x'.
Remove the zero:
-182x + -202x2 + 288x3 + -72x4 = 182x + 202x2 + -288x3 + 72x4 + -182x + -202x2 + 288x3 + -72x4

Reorder the terms:
-182x + -202x2 + 288x3 + -72x4 = 182x + -182x + 202x2 + -202x2 + -288x3 + 288x3 + 72x4 + -72x4

Combine like terms: 182x + -182x = 0
-182x + -202x2 + 288x3 + -72x4 = 0 + 202x2 + -202x2 + -288x3 + 288x3 + 72x4 + -72x4
-182x + -202x2 + 288x3 + -72x4 = 202x2 + -202x2 + -288x3 + 288x3 + 72x4 + -72x4

Combine like terms: 202x2 + -202x2 = 0
-182x + -202x2 + 288x3 + -72x4 = 0 + -288x3 + 288x3 + 72x4 + -72x4
-182x + -202x2 + 288x3 + -72x4 = -288x3 + 288x3 + 72x4 + -72x4

Combine like terms: -288x3 + 288x3 = 0
-182x + -202x2 + 288x3 + -72x4 = 0 + 72x4 + -72x4
-182x + -202x2 + 288x3 + -72x4 = 72x4 + -72x4

Combine like terms: 72x4 + -72x4 = 0
-182x + -202x2 + 288x3 + -72x4 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-91 + -101x + 144x2 + -36x3) = 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 '(-91 + -101x + 144x2 + -36x3)' equal to zero and attempt to solve:

Simplifying
-91 + -101x + 144x2 + -36x3 = 0

Solving
-91 + -101x + 144x2 + -36x3 = 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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