(6x^3+7x^2-3x)(x^2-7)=0

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


Simplifying
(6x3 + 7x2 + -3x)(x2 + -7) = 0

Reorder the terms:
(-3x + 7x2 + 6x3)(x2 + -7) = 0

Reorder the terms:
(-3x + 7x2 + 6x3)(-7 + x2) = 0

Multiply (-3x + 7x2 + 6x3) * (-7 + x2)
(-3x * (-7 + x2) + 7x2 * (-7 + x2) + 6x3 * (-7 + x2)) = 0
((-7 * -3x + x2 * -3x) + 7x2 * (-7 + x2) + 6x3 * (-7 + x2)) = 0
((21x + -3x3) + 7x2 * (-7 + x2) + 6x3 * (-7 + x2)) = 0
(21x + -3x3 + (-7 * 7x2 + x2 * 7x2) + 6x3 * (-7 + x2)) = 0
(21x + -3x3 + (-49x2 + 7x4) + 6x3 * (-7 + x2)) = 0
(21x + -3x3 + -49x2 + 7x4 + (-7 * 6x3 + x2 * 6x3)) = 0
(21x + -3x3 + -49x2 + 7x4 + (-42x3 + 6x5)) = 0

Reorder the terms:
(21x + -49x2 + -3x3 + -42x3 + 7x4 + 6x5) = 0

Combine like terms: -3x3 + -42x3 = -45x3
(21x + -49x2 + -45x3 + 7x4 + 6x5) = 0

Solving
21x + -49x2 + -45x3 + 7x4 + 6x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(21 + -49x + -45x2 + 7x3 + 6x4) = 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 '(21 + -49x + -45x2 + 7x3 + 6x4)' equal to zero and attempt to solve:

Simplifying
21 + -49x + -45x2 + 7x3 + 6x4 = 0

Solving
21 + -49x + -45x2 + 7x3 + 6x4 = 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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