R^2-4R-1=20

Solution for R^2-4R-1=20 equation:

Simplifying
R2 + -4R + -1 = 20

Reorder the terms:
-1 + -4R + R2 = 20

Solving
-1 + -4R + R2 = 20

Solving for variable 'R'.

Reorder the terms:
-1 + -20 + -4R + R2 = 20 + -20

Combine like terms: -1 + -20 = -21
-21 + -4R + R2 = 20 + -20

Combine like terms: 20 + -20 = 0
-21 + -4R + R2 = 0

Factor a trinomial.
(-3 + -1R)(7 + -1R) = 0

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

Simplifying
-3 + -1R = 0

Solving
-3 + -1R = 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 + -1R = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1R = 0 + 3
-1R = 0 + 3

Combine like terms: 0 + 3 = 3
-1R = 3

Divide each side by '-1'.
R = -3

Simplifying
R = -3
Subproblem 2
Set the factor '(7 + -1R)' equal to zero and attempt to solve:

Simplifying
7 + -1R = 0

Solving
7 + -1R = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1R = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1R = 0 + -7
-1R = 0 + -7

Combine like terms: 0 + -7 = -7
-1R = -7

Divide each side by '-1'.
R = 7

Simplifying
R = 7
Solution
R = {-3, 7}