r^2-45=-5-6r

Solution for r^2-45=-5-6r equation:

Simplifying
r2 + -45 = -5 + -6r

Reorder the terms:
-45 + r2 = -5 + -6r

Solving
-45 + r2 = -5 + -6r

Solving for variable 'r'.

Reorder the terms:
-45 + 5 + 6r + r2 = -5 + -6r + 5 + 6r

Combine like terms: -45 + 5 = -40
-40 + 6r + r2 = -5 + -6r + 5 + 6r

Reorder the terms:
-40 + 6r + r2 = -5 + 5 + -6r + 6r

Combine like terms: -5 + 5 = 0
-40 + 6r + r2 = 0 + -6r + 6r
-40 + 6r + r2 = -6r + 6r

Combine like terms: -6r + 6r = 0
-40 + 6r + r2 = 0

Factor a trinomial.
(-10 + -1r)(4 + -1r) = 0

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

Simplifying
-10 + -1r = 0

Solving
-10 + -1r = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1r = 0 + 10

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

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

Divide each side by '-1'.
r = -10

Simplifying
r = -10
Subproblem 2
Set the factor '(4 + -1r)' equal to zero and attempt to solve:

Simplifying
4 + -1r = 0

Solving
4 + -1r = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1r = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1r = 0 + -4
-1r = 0 + -4

Combine like terms: 0 + -4 = -4
-1r = -4

Divide each side by '-1'.
r = 4

Simplifying
r = 4
Solution
r = {-10, 4}