40r^2-42r+9=0

Solution for 40r^2-42r+9=0 equation:

Simplifying
40r2 + -42r + 9 = 0

Reorder the terms:
9 + -42r + 40r2 = 0

Solving
9 + -42r + 40r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(3 + -10r)(3 + -4r) = 0

Subproblem 1
Set the factor '(3 + -10r)' equal to zero and attempt to solve:

Simplifying
3 + -10r = 0

Solving
3 + -10r = 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 + -10r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -10r = 0 + -3
-10r = 0 + -3

Combine like terms: 0 + -3 = -3
-10r = -3

Divide each side by '-10'.
r = 0.3

Simplifying
r = 0.3
Subproblem 2
Set the factor '(3 + -4r)' equal to zero and attempt to solve:

Simplifying
3 + -4r = 0

Solving
3 + -4r = 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 + -4r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4r = 0 + -3
-4r = 0 + -3

Combine like terms: 0 + -3 = -3
-4r = -3

Divide each side by '-4'.
r = 0.75

Simplifying
r = 0.75
Solution
r = {0.3, 0.75}