5r^2+42r=27

Solution for 5r^2+42r=27 equation:

Simplifying
5r2 + 42r = 27

Reorder the terms:
42r + 5r2 = 27

Solving
42r + 5r2 = 27

Solving for variable 'r'.

Reorder the terms:
-27 + 42r + 5r2 = 27 + -27

Combine like terms: 27 + -27 = 0
-27 + 42r + 5r2 = 0

Factor a trinomial.
(-9 + -1r)(3 + -5r) = 0

Subproblem 1
Set the factor '(-9 + -1r)' equal to zero and attempt to solve:

Simplifying
-9 + -1r = 0

Solving
-9 + -1r = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1r = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1r = 0 + 9
-1r = 0 + 9

Combine like terms: 0 + 9 = 9
-1r = 9

Divide each side by '-1'.
r = -9

Simplifying
r = -9
Subproblem 2
Set the factor '(3 + -5r)' equal to zero and attempt to solve:

Simplifying
3 + -5r = 0

Solving
3 + -5r = 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 + -5r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5r = 0 + -3
-5r = 0 + -3

Combine like terms: 0 + -3 = -3
-5r = -3

Divide each side by '-5'.
r = 0.6

Simplifying
r = 0.6
Solution
r = {-9, 0.6}