R^2+R=42

Solution for R^2+R=42 equation:

Simplifying
R2 + R = 42

Reorder the terms:
R + R2 = 42

Solving
R + R2 = 42

Solving for variable 'R'.

Reorder the terms:
-42 + R + R2 = 42 + -42

Combine like terms: 42 + -42 = 0
-42 + R + R2 = 0

Factor a trinomial.
(-7 + -1R)(6 + -1R) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(6 + -1R)' equal to zero and attempt to solve:

Simplifying
6 + -1R = 0

Solving
6 + -1R = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1R = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1R = 0 + -6
-1R = 0 + -6

Combine like terms: 0 + -6 = -6
-1R = -6

Divide each side by '-1'.
R = 6

Simplifying
R = 6
Solution
R = {-7, 6}