(-4r^3)(8r^2+7)(8r^2-7)=

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Solution for (-4r^3)(8r^2+7)(8r^2-7)= equation: 


Simplifying
(-4r3)(8r2 + 7)(8r2 + -7) = 0

Remove parenthesis around (-4r3)
-4r3(8r2 + 7)(8r2 + -7) = 0

Reorder the terms:
-4r3(7 + 8r2)(8r2 + -7) = 0

Reorder the terms:
-4r3(7 + 8r2)(-7 + 8r2) = 0

Multiply (7 + 8r2) * (-7 + 8r2)
-4r3(7(-7 + 8r2) + 8r2 * (-7 + 8r2)) = 0
-4r3((-7 * 7 + 8r2 * 7) + 8r2 * (-7 + 8r2)) = 0
-4r3((-49 + 56r2) + 8r2 * (-7 + 8r2)) = 0
-4r3(-49 + 56r2 + (-7 * 8r2 + 8r2 * 8r2)) = 0
-4r3(-49 + 56r2 + (-56r2 + 64r4)) = 0

Combine like terms: 56r2 + -56r2 = 0
-4r3(-49 + 0 + 64r4) = 0
-4r3(-49 + 64r4) = 0
(-49 * -4r3 + 64r4 * -4r3) = 0
(196r3 + -256r7) = 0

Solving
196r3 + -256r7 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '4r3'.
4r3(49 + -64r4) = 0

Factor a difference between two squares.
4r3((7 + 8r2)(7 + -8r2)) = 0

Ignore the factor 4.

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 '(7 + 8r2)' equal to zero and attempt to solve:

Simplifying
7 + 8r2 = 0

Solving
7 + 8r2 = 0

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

Add '-7' to each side of the equation.
7 + -7 + 8r2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 8r2 = 0 + -7
8r2 = 0 + -7

Combine like terms: 0 + -7 = -7
8r2 = -7

Divide each side by '8'.
r2 = -0.875

Simplifying
r2 = -0.875

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 '(7 + -8r2)' equal to zero and attempt to solve:

Simplifying
7 + -8r2 = 0

Solving
7 + -8r2 = 0

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

Add '-7' to each side of the equation.
7 + -7 + -8r2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -8r2 = 0 + -7
-8r2 = 0 + -7

Combine like terms: 0 + -7 = -7
-8r2 = -7

Divide each side by '-8'.
r2 = 0.875

Simplifying
r2 = 0.875

Take the square root of each side:
r = {-0.935414347, 0.935414347}
Solution
r = {-0.935414347, 0.935414347}

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