4r^2+31r+42=0

Solution for 4r^2+31r+42=0 equation:

Simplifying
4r2 + 31r + 42 = 0

Reorder the terms:
42 + 31r + 4r2 = 0

Solving
42 + 31r + 4r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(6 + r)(7 + 4r) = 0

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

Simplifying
6 + r = 0

Solving
6 + r = 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 + r = 0 + -6

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

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

Simplifying
r = -6
Subproblem 2
Set the factor '(7 + 4r)' equal to zero and attempt to solve:

Simplifying
7 + 4r = 0

Solving
7 + 4r = 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 + 4r = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 4r = 0 + -7
4r = 0 + -7

Combine like terms: 0 + -7 = -7
4r = -7

Divide each side by '4'.
r = -1.75

Simplifying
r = -1.75
Solution
r = {-6, -1.75}