3x(x+1)(2x-7)(3x+4)(x-13)(x+7)=0

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Solution for 3x(x+1)(2x-7)(3x+4)(x-13)(x+7)=0 equation: 


Simplifying
3x(x + 1)(2x + -7)(3x + 4)(x + -13)(x + 7) = 0

Reorder the terms:
3x(1 + x)(2x + -7)(3x + 4)(x + -13)(x + 7) = 0

Reorder the terms:
3x(1 + x)(-7 + 2x)(3x + 4)(x + -13)(x + 7) = 0

Reorder the terms:
3x(1 + x)(-7 + 2x)(4 + 3x)(x + -13)(x + 7) = 0

Reorder the terms:
3x(1 + x)(-7 + 2x)(4 + 3x)(-13 + x)(x + 7) = 0

Reorder the terms:
3x(1 + x)(-7 + 2x)(4 + 3x)(-13 + x)(7 + x) = 0

Multiply (1 + x) * (-7 + 2x)
3x(1(-7 + 2x) + x(-7 + 2x))(4 + 3x)(-13 + x)(7 + x) = 0
3x((-7 * 1 + 2x * 1) + x(-7 + 2x))(4 + 3x)(-13 + x)(7 + x) = 0
3x((-7 + 2x) + x(-7 + 2x))(4 + 3x)(-13 + x)(7 + x) = 0
3x(-7 + 2x + (-7 * x + 2x * x))(4 + 3x)(-13 + x)(7 + x) = 0
3x(-7 + 2x + (-7x + 2x2))(4 + 3x)(-13 + x)(7 + x) = 0

Combine like terms: 2x + -7x = -5x
3x(-7 + -5x + 2x2)(4 + 3x)(-13 + x)(7 + x) = 0

Multiply (-7 + -5x + 2x2) * (4 + 3x)
3x(-7(4 + 3x) + -5x * (4 + 3x) + 2x2 * (4 + 3x))(-13 + x)(7 + x) = 0
3x((4 * -7 + 3x * -7) + -5x * (4 + 3x) + 2x2 * (4 + 3x))(-13 + x)(7 + x) = 0
3x((-28 + -21x) + -5x * (4 + 3x) + 2x2 * (4 + 3x))(-13 + x)(7 + x) = 0
3x(-28 + -21x + (4 * -5x + 3x * -5x) + 2x2 * (4 + 3x))(-13 + x)(7 + x) = 0
3x(-28 + -21x + (-20x + -15x2) + 2x2 * (4 + 3x))(-13 + x)(7 + x) = 0
3x(-28 + -21x + -20x + -15x2 + (4 * 2x2 + 3x * 2x2))(-13 + x)(7 + x) = 0
3x(-28 + -21x + -20x + -15x2 + (8x2 + 6x3))(-13 + x)(7 + x) = 0

Combine like terms: -21x + -20x = -41x
3x(-28 + -41x + -15x2 + 8x2 + 6x3)(-13 + x)(7 + x) = 0

Combine like terms: -15x2 + 8x2 = -7x2
3x(-28 + -41x + -7x2 + 6x3)(-13 + x)(7 + x) = 0

Multiply (-28 + -41x + -7x2 + 6x3) * (-13 + x)
3x(-28(-13 + x) + -41x * (-13 + x) + -7x2 * (-13 + x) + 6x3 * (-13 + x))(7 + x) = 0
3x((-13 * -28 + x * -28) + -41x * (-13 + x) + -7x2 * (-13 + x) + 6x3 * (-13 + x))(7 + x) = 0
3x((364 + -28x) + -41x * (-13 + x) + -7x2 * (-13 + x) + 6x3 * (-13 + x))(7 + x) = 0
3x(364 + -28x + (-13 * -41x + x * -41x) + -7x2 * (-13 + x) + 6x3 * (-13 + x))(7 + x) = 0
3x(364 + -28x + (533x + -41x2) + -7x2 * (-13 + x) + 6x3 * (-13 + x))(7 + x) = 0
3x(364 + -28x + 533x + -41x2 + (-13 * -7x2 + x * -7x2) + 6x3 * (-13 + x))(7 + x) = 0
3x(364 + -28x + 533x + -41x2 + (91x2 + -7x3) + 6x3 * (-13 + x))(7 + x) = 0
3x(364 + -28x + 533x + -41x2 + 91x2 + -7x3 + (-13 * 6x3 + x * 6x3))(7 + x) = 0
3x(364 + -28x + 533x + -41x2 + 91x2 + -7x3 + (-78x3 + 6x4))(7 + x) = 0

Combine like terms: -28x + 533x = 505x
3x(364 + 505x + -41x2 + 91x2 + -7x3 + -78x3 + 6x4)(7 + x) = 0

Combine like terms: -41x2 + 91x2 = 50x2
3x(364 + 505x + 50x2 + -7x3 + -78x3 + 6x4)(7 + x) = 0

Combine like terms: -7x3 + -78x3 = -85x3
3x(364 + 505x + 50x2 + -85x3 + 6x4)(7 + x) = 0

Multiply (364 + 505x + 50x2 + -85x3 + 6x4) * (7 + x)
3x(364(7 + x) + 505x * (7 + x) + 50x2 * (7 + x) + -85x3 * (7 + x) + 6x4 * (7 + x)) = 0
3x((7 * 364 + x * 364) + 505x * (7 + x) + 50x2 * (7 + x) + -85x3 * (7 + x) + 6x4 * (7 + x)) = 0
3x((2548 + 364x) + 505x * (7 + x) + 50x2 * (7 + x) + -85x3 * (7 + x) + 6x4 * (7 + x)) = 0
3x(2548 + 364x + (7 * 505x + x * 505x) + 50x2 * (7 + x) + -85x3 * (7 + x) + 6x4 * (7 + x)) = 0
3x(2548 + 364x + (3535x + 505x2) + 50x2 * (7 + x) + -85x3 * (7 + x) + 6x4 * (7 + x)) = 0
3x(2548 + 364x + 3535x + 505x2 + (7 * 50x2 + x * 50x2) + -85x3 * (7 + x) + 6x4 * (7 + x)) = 0
3x(2548 + 364x + 3535x + 505x2 + (350x2 + 50x3) + -85x3 * (7 + x) + 6x4 * (7 + x)) = 0
3x(2548 + 364x + 3535x + 505x2 + 350x2 + 50x3 + (7 * -85x3 + x * -85x3) + 6x4 * (7 + x)) = 0
3x(2548 + 364x + 3535x + 505x2 + 350x2 + 50x3 + (-595x3 + -85x4) + 6x4 * (7 + x)) = 0
3x(2548 + 364x + 3535x + 505x2 + 350x2 + 50x3 + -595x3 + -85x4 + (7 * 6x4 + x * 6x4)) = 0
3x(2548 + 364x + 3535x + 505x2 + 350x2 + 50x3 + -595x3 + -85x4 + (42x4 + 6x5)) = 0

Combine like terms: 364x + 3535x = 3899x
3x(2548 + 3899x + 505x2 + 350x2 + 50x3 + -595x3 + -85x4 + 42x4 + 6x5) = 0

Combine like terms: 505x2 + 350x2 = 855x2
3x(2548 + 3899x + 855x2 + 50x3 + -595x3 + -85x4 + 42x4 + 6x5) = 0

Combine like terms: 50x3 + -595x3 = -545x3
3x(2548 + 3899x + 855x2 + -545x3 + -85x4 + 42x4 + 6x5) = 0

Combine like terms: -85x4 + 42x4 = -43x4
3x(2548 + 3899x + 855x2 + -545x3 + -43x4 + 6x5) = 0
(2548 * 3x + 3899x * 3x + 855x2 * 3x + -545x3 * 3x + -43x4 * 3x + 6x5 * 3x) = 0
(7644x + 11697x2 + 2565x3 + -1635x4 + -129x5 + 18x6) = 0

Solving
7644x + 11697x2 + 2565x3 + -1635x4 + -129x5 + 18x6 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(2548 + 3899x + 855x2 + -545x3 + -43x4 + 6x5) = 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 '(2548 + 3899x + 855x2 + -545x3 + -43x4 + 6x5)' equal to zero and attempt to solve:

Simplifying
2548 + 3899x + 855x2 + -545x3 + -43x4 + 6x5 = 0

Solving
2548 + 3899x + 855x2 + -545x3 + -43x4 + 6x5 = 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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