5r^2=-42-41r

Solution for 5r^2=-42-41r equation:

Simplifying
5r2 = -42 + -41r

Solving
5r2 = -42 + -41r

Solving for variable 'r'.

Reorder the terms:
42 + 41r + 5r2 = -42 + -41r + 42 + 41r

Reorder the terms:
42 + 41r + 5r2 = -42 + 42 + -41r + 41r

Combine like terms: -42 + 42 = 0
42 + 41r + 5r2 = 0 + -41r + 41r
42 + 41r + 5r2 = -41r + 41r

Combine like terms: -41r + 41r = 0
42 + 41r + 5r2 = 0

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

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

Simplifying
7 + r = 0

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

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

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

Simplifying
r = -7
Subproblem 2
Set the factor '(6 + 5r)' equal to zero and attempt to solve:

Simplifying
6 + 5r = 0

Solving
6 + 5r = 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 + 5r = 0 + -6

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

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

Divide each side by '5'.
r = -1.2

Simplifying
r = -1.2
Solution
r = {-7, -1.2}