25r^2-45r+14=6

Solution for 25r^2-45r+14=6 equation:

Simplifying
25r2 + -45r + 14 = 6

Reorder the terms:
14 + -45r + 25r2 = 6

Solving
14 + -45r + 25r2 = 6

Solving for variable 'r'.

Reorder the terms:
14 + -6 + -45r + 25r2 = 6 + -6

Combine like terms: 14 + -6 = 8
8 + -45r + 25r2 = 6 + -6

Combine like terms: 6 + -6 = 0
8 + -45r + 25r2 = 0

Factor a trinomial.
(1 + -5r)(8 + -5r) = 0

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

Simplifying
1 + -5r = 0

Solving
1 + -5r = 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 + -5r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5r = 0 + -1
-5r = 0 + -1

Combine like terms: 0 + -1 = -1
-5r = -1

Divide each side by '-5'.
r = 0.2

Simplifying
r = 0.2
Subproblem 2
Set the factor '(8 + -5r)' equal to zero and attempt to solve:

Simplifying
8 + -5r = 0

Solving
8 + -5r = 0

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

Add '-8' to each side of the equation.
8 + -8 + -5r = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -5r = 0 + -8
-5r = 0 + -8

Combine like terms: 0 + -8 = -8
-5r = -8

Divide each side by '-5'.
r = 1.6

Simplifying
r = 1.6
Solution
r = {0.2, 1.6}