r^2+18r+52=7

Solution for r^2+18r+52=7 equation:

Simplifying
r2 + 18r + 52 = 7

Reorder the terms:
52 + 18r + r2 = 7

Solving
52 + 18r + r2 = 7

Solving for variable 'r'.

Reorder the terms:
52 + -7 + 18r + r2 = 7 + -7

Combine like terms: 52 + -7 = 45
45 + 18r + r2 = 7 + -7

Combine like terms: 7 + -7 = 0
45 + 18r + r2 = 0

Factor a trinomial.
(15 + r)(3 + r) = 0

Subproblem 1
Set the factor '(15 + r)' equal to zero and attempt to solve:

Simplifying
15 + r = 0

Solving
15 + r = 0

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

Add '-15' to each side of the equation.
15 + -15 + r = 0 + -15

Combine like terms: 15 + -15 = 0
0 + r = 0 + -15
r = 0 + -15

Combine like terms: 0 + -15 = -15
r = -15

Simplifying
r = -15
Subproblem 2
Set the factor '(3 + r)' equal to zero and attempt to solve:

Simplifying
3 + r = 0

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

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

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

Simplifying
r = -3
Solution
r = {-15, -3}