5r^2+9r-14=0

Solution for 5r^2+9r-14=0 equation:

Simplifying
5r2 + 9r + -14 = 0

Reorder the terms:
-14 + 9r + 5r2 = 0

Solving
-14 + 9r + 5r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-14 + -5r)(1 + -1r) = 0

Subproblem 1
Set the factor '(-14 + -5r)' equal to zero and attempt to solve:

Simplifying
-14 + -5r = 0

Solving
-14 + -5r = 0

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

Add '14' to each side of the equation.
-14 + 14 + -5r = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -5r = 0 + 14
-5r = 0 + 14

Combine like terms: 0 + 14 = 14
-5r = 14

Divide each side by '-5'.
r = -2.8

Simplifying
r = -2.8
Subproblem 2
Set the factor '(1 + -1r)' equal to zero and attempt to solve:

Simplifying
1 + -1r = 0

Solving
1 + -1r = 0

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

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

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

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

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

Simplifying
r = 1
Solution
r = {-2.8, 1}