6r^3+36r^2=42r

Solution for 6r^3+36r^2=42r equation:

Simplifying
6r3 + 36r2 = 42r

Reorder the terms:
36r2 + 6r3 = 42r

Solving
36r2 + 6r3 = 42r

Solving for variable 'r'.

Reorder the terms:
-42r + 36r2 + 6r3 = 42r + -42r

Combine like terms: 42r + -42r = 0
-42r + 36r2 + 6r3 = 0

Factor out the Greatest Common Factor (GCF), '6r'.
6r(-7 + 6r + r2) = 0

Factor a trinomial.
6r((-7 + -1r)(1 + -1r)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor 'r' equal to zero and attempt to solve:

Simplifying
r = 0

Solving
r = 0

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

Simplifying
r = 0
Subproblem 2
Set the factor '(-7 + -1r)' equal to zero and attempt to solve:

Simplifying
-7 + -1r = 0

Solving
-7 + -1r = 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 + -1r = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1r = 0 + 7
-1r = 0 + 7

Combine like terms: 0 + 7 = 7
-1r = 7

Divide each side by '-1'.
r = -7

Simplifying
r = -7
Subproblem 3
Set the factor '(1 + -1r)' equal to zero and attempt to solve:

Simplifying
1 + -1r = 0

Solving
1 + -1r = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1r = 0 + -1
-1r = 0 + -1

Combine like terms: 0 + -1 = -1
-1r = -1

Divide each side by '-1'.
r = 1

Simplifying
r = 1
Solution
r = {0, -7, 1}