25r^2-5r-14=-2

Solution for 25r^2-5r-14=-2 equation:

Simplifying
25r2 + -5r + -14 = -2

Reorder the terms:
-14 + -5r + 25r2 = -2

Solving
-14 + -5r + 25r2 = -2

Solving for variable 'r'.

Reorder the terms:
-14 + 2 + -5r + 25r2 = -2 + 2

Combine like terms: -14 + 2 = -12
-12 + -5r + 25r2 = -2 + 2

Combine like terms: -2 + 2 = 0
-12 + -5r + 25r2 = 0

Factor a trinomial.
(-3 + -5r)(4 + -5r) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(4 + -5r)' equal to zero and attempt to solve:

Simplifying
4 + -5r = 0

Solving
4 + -5r = 0

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

Add '-4' to each side of the equation.
4 + -4 + -5r = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5r = 0 + -4
-5r = 0 + -4

Combine like terms: 0 + -4 = -4
-5r = -4

Divide each side by '-5'.
r = 0.8

Simplifying
r = 0.8
Solution
r = {-0.6, 0.8}