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

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


Simplifying
3x2(x2 + -7) + -1x3(2x) = 0

Reorder the terms:
3x2(-7 + x2) + -1x3(2x) = 0
(-7 * 3x2 + x2 * 3x2) + -1x3(2x) = 0
(-21x2 + 3x4) + -1x3(2x) = 0

Remove parenthesis around (2x)
-21x2 + 3x4 + -1x3 * 2x = 0

Reorder the terms for easier multiplication:
-21x2 + 3x4 + -1 * 2x3 * x = 0

Multiply -1 * 2
-21x2 + 3x4 + -2x3 * x = 0

Multiply x3 * x
-21x2 + 3x4 + -2x4 = 0

Combine like terms: 3x4 + -2x4 = 1x4
-21x2 + 1x4 = 0

Solving
-21x2 + 1x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-21 + x2) = 0


Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}

Subproblem 2
Set the factor '(-21 + x2)' equal to zero and attempt to solve:

Simplifying
-21 + x2 = 0

Solving
-21 + x2 = 0

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

Add '21' to each side of the equation.
-21 + 21 + x2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + x2 = 0 + 21
x2 = 0 + 21

Combine like terms: 0 + 21 = 21
x2 = 21

Simplifying
x2 = 21

Take the square root of each side:
x = {-4.582575695, 4.582575695}
Solution
x = {0, -4.582575695, 4.582575695}

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