20r^2-28r-3=0

Solution for 20r^2-28r-3=0 equation:

Simplifying
20r2 + -28r + -3 = 0

Reorder the terms:
-3 + -28r + 20r2 = 0

Solving
-3 + -28r + 20r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-1 + -10r)(3 + -2r) = 0

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

Simplifying
-1 + -10r = 0

Solving
-1 + -10r = 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 + -10r = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -10r = 0 + 1
-10r = 0 + 1

Combine like terms: 0 + 1 = 1
-10r = 1

Divide each side by '-10'.
r = -0.1

Simplifying
r = -0.1
Subproblem 2
Set the factor '(3 + -2r)' equal to zero and attempt to solve:

Simplifying
3 + -2r = 0

Solving
3 + -2r = 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 + -2r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2r = 0 + -3
-2r = 0 + -3

Combine like terms: 0 + -3 = -3
-2r = -3

Divide each side by '-2'.
r = 1.5

Simplifying
r = 1.5
Solution
r = {-0.1, 1.5}