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

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


Simplifying
r2(3r + 2)(3r + -2) = 0

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

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

Multiply (2 + 3r) * (-2 + 3r)
r2(2(-2 + 3r) + 3r * (-2 + 3r)) = 0
r2((-2 * 2 + 3r * 2) + 3r * (-2 + 3r)) = 0
r2((-4 + 6r) + 3r * (-2 + 3r)) = 0
r2(-4 + 6r + (-2 * 3r + 3r * 3r)) = 0
r2(-4 + 6r + (-6r + 9r2)) = 0

Combine like terms: 6r + -6r = 0
r2(-4 + 0 + 9r2) = 0
r2(-4 + 9r2) = 0
(-4 * r2 + 9r2 * r2) = 0
(-4r2 + 9r4) = 0

Solving
-4r2 + 9r4 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), 'r2'.
r2(-4 + 9r2) = 0

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


Subproblem 1
Set the factor 'r2' equal to zero and attempt to solve:

Simplifying
r2 = 0

Solving
r2 = 0

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

Simplifying
r2 = 0

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

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

Simplifying
2 + 3r = 0

Solving
2 + 3r = 0

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

Add '-2' to each side of the equation.
2 + -2 + 3r = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3r = 0 + -2
3r = 0 + -2

Combine like terms: 0 + -2 = -2
3r = -2

Divide each side by '3'.
r = -0.6666666667

Simplifying
r = -0.6666666667

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

Simplifying
-2 + 3r = 0

Solving
-2 + 3r = 0

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

Add '2' to each side of the equation.
-2 + 2 + 3r = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 3r = 0 + 2
3r = 0 + 2

Combine like terms: 0 + 2 = 2
3r = 2

Divide each side by '3'.
r = 0.6666666667

Simplifying
r = 0.6666666667
Solution
r = {0, -0.6666666667, 0.6666666667}

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