3r(r^2+4r-21r)=0

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Solution for 3r(r^2+4r-21r)=0 equation: 


Simplifying
3r(r2 + 4r + -21r) = 0

Reorder the terms:
3r(4r + -21r + r2) = 0

Combine like terms: 4r + -21r = -17r
3r(-17r + r2) = 0
(-17r * 3r + r2 * 3r) = 0
(-51r2 + 3r3) = 0

Solving
-51r2 + 3r3 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '3r2'.
3r2(-17 + r) = 0

Ignore the factor 3.

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 '(-17 + r)' equal to zero and attempt to solve:

Simplifying
-17 + r = 0

Solving
-17 + r = 0

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

Add '17' to each side of the equation.
-17 + 17 + r = 0 + 17

Combine like terms: -17 + 17 = 0
0 + r = 0 + 17
r = 0 + 17

Combine like terms: 0 + 17 = 17
r = 17

Simplifying
r = 17
Solution
r = {0, 17}

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