6r^2+32r+42=

Solution for 6r^2+32r+42= equation:

Simplifying
6r2 + 32r + 42 = 0

Reorder the terms:
42 + 32r + 6r2 = 0

Solving
42 + 32r + 6r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2'.
2(21 + 16r + 3r2) = 0

Factor a trinomial.
2((3 + r)(7 + 3r)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + r)' equal to zero and attempt to solve:

Simplifying
3 + r = 0

Solving
3 + r = 0

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

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

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

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

Simplifying
r = -3
Subproblem 2
Set the factor '(7 + 3r)' equal to zero and attempt to solve:

Simplifying
7 + 3r = 0

Solving
7 + 3r = 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 + 3r = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3r = 0 + -7
3r = 0 + -7

Combine like terms: 0 + -7 = -7
3r = -7

Divide each side by '3'.
r = -2.333333333

Simplifying
r = -2.333333333
Solution
r = {-3, -2.333333333}