-2r^3(3r^2+4)(3r^2-4)=

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Solution for -2r^3(3r^2+4)(3r^2-4)= equation: 


Simplifying
-2r3(3r2 + 4)(3r2 + -4) = 0

Reorder the terms:
-2r3(4 + 3r2)(3r2 + -4) = 0

Reorder the terms:
-2r3(4 + 3r2)(-4 + 3r2) = 0

Multiply (4 + 3r2) * (-4 + 3r2)
-2r3(4(-4 + 3r2) + 3r2 * (-4 + 3r2)) = 0
-2r3((-4 * 4 + 3r2 * 4) + 3r2 * (-4 + 3r2)) = 0
-2r3((-16 + 12r2) + 3r2 * (-4 + 3r2)) = 0
-2r3(-16 + 12r2 + (-4 * 3r2 + 3r2 * 3r2)) = 0
-2r3(-16 + 12r2 + (-12r2 + 9r4)) = 0

Combine like terms: 12r2 + -12r2 = 0
-2r3(-16 + 0 + 9r4) = 0
-2r3(-16 + 9r4) = 0
(-16 * -2r3 + 9r4 * -2r3) = 0
(32r3 + -18r7) = 0

Solving
32r3 + -18r7 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2r3'.
2r3(16 + -9r4) = 0

Factor a difference between two squares.
2r3((4 + 3r2)(4 + -3r2)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'r3' equal to zero and attempt to solve:

Simplifying
r3 = 0

Solving
r3 = 0

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

Simplifying
r3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(4 + 3r2)' equal to zero and attempt to solve:

Simplifying
4 + 3r2 = 0

Solving
4 + 3r2 = 0

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

Add '-4' to each side of the equation.
4 + -4 + 3r2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3r2 = 0 + -4
3r2 = 0 + -4

Combine like terms: 0 + -4 = -4
3r2 = -4

Divide each side by '3'.
r2 = -1.333333333

Simplifying
r2 = -1.333333333

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 3
Set the factor '(4 + -3r2)' equal to zero and attempt to solve:

Simplifying
4 + -3r2 = 0

Solving
4 + -3r2 = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3r2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3r2 = 0 + -4
-3r2 = 0 + -4

Combine like terms: 0 + -4 = -4
-3r2 = -4

Divide each side by '-3'.
r2 = 1.333333333

Simplifying
r2 = 1.333333333

Take the square root of each side:
r = {-1.154700538, 1.154700538}
Solution
r = {-1.154700538, 1.154700538}

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