15r^2-43r=-30

Solution for 15r^2-43r=-30 equation:

Simplifying
15r2 + -43r = -30

Reorder the terms:
-43r + 15r2 = -30

Solving
-43r + 15r2 = -30

Solving for variable 'r'.

Reorder the terms:
30 + -43r + 15r2 = -30 + 30

Combine like terms: -30 + 30 = 0
30 + -43r + 15r2 = 0

Factor a trinomial.
(6 + -5r)(5 + -3r) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(5 + -3r)' equal to zero and attempt to solve:

Simplifying
5 + -3r = 0

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

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

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

Divide each side by '-3'.
r = 1.666666667

Simplifying
r = 1.666666667
Solution
r = {1.2, 1.666666667}