42*r^2+r=30

Solution for 42*r^2+r=30 equation:

Simplifying
42r2 + r = 30

Reorder the terms:
r + 42r2 = 30

Solving
r + 42r2 = 30

Solving for variable 'r'.

Reorder the terms:
-30 + r + 42r2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + r + 42r2 = 0

Factor a trinomial.
(-6 + -7r)(5 + -6r) = 0

Subproblem 1
Set the factor '(-6 + -7r)' equal to zero and attempt to solve:

Simplifying
-6 + -7r = 0

Solving
-6 + -7r = 0

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

Add '6' to each side of the equation.
-6 + 6 + -7r = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -7r = 0 + 6
-7r = 0 + 6

Combine like terms: 0 + 6 = 6
-7r = 6

Divide each side by '-7'.
r = -0.8571428571

Simplifying
r = -0.8571428571
Subproblem 2
Set the factor '(5 + -6r)' equal to zero and attempt to solve:

Simplifying
5 + -6r = 0

Solving
5 + -6r = 0

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

Add '-5' to each side of the equation.
5 + -5 + -6r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -6r = 0 + -5
-6r = 0 + -5

Combine like terms: 0 + -5 = -5
-6r = -5

Divide each side by '-6'.
r = 0.8333333333

Simplifying
r = 0.8333333333
Solution
r = {-0.8571428571, 0.8333333333}