(2r+2)(2r+2)=169

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Solution for (2r+2)(2r+2)=169 equation: 


Simplifying
(2r + 2)(2r + 2) = 169

Reorder the terms:
(2 + 2r)(2r + 2) = 169

Reorder the terms:
(2 + 2r)(2 + 2r) = 169

Multiply (2 + 2r) * (2 + 2r)
(2(2 + 2r) + 2r * (2 + 2r)) = 169
((2 * 2 + 2r * 2) + 2r * (2 + 2r)) = 169
((4 + 4r) + 2r * (2 + 2r)) = 169
(4 + 4r + (2 * 2r + 2r * 2r)) = 169
(4 + 4r + (4r + 4r2)) = 169

Combine like terms: 4r + 4r = 8r
(4 + 8r + 4r2) = 169

Solving
4 + 8r + 4r2 = 169

Solving for variable 'r'.

Reorder the terms:
4 + -169 + 8r + 4r2 = 169 + -169

Combine like terms: 4 + -169 = -165
-165 + 8r + 4r2 = 169 + -169

Combine like terms: 169 + -169 = 0
-165 + 8r + 4r2 = 0

Factor a trinomial.
(-15 + -2r)(11 + -2r) = 0


Subproblem 1
Set the factor '(-15 + -2r)' equal to zero and attempt to solve:

Simplifying
-15 + -2r = 0

Solving
-15 + -2r = 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 + -2r = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -2r = 0 + 15
-2r = 0 + 15

Combine like terms: 0 + 15 = 15
-2r = 15

Divide each side by '-2'.
r = -7.5

Simplifying
r = -7.5

Subproblem 2
Set the factor '(11 + -2r)' equal to zero and attempt to solve:

Simplifying
11 + -2r = 0

Solving
11 + -2r = 0

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

Add '-11' to each side of the equation.
11 + -11 + -2r = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -2r = 0 + -11
-2r = 0 + -11

Combine like terms: 0 + -11 = -11
-2r = -11

Divide each side by '-2'.
r = 5.5

Simplifying
r = 5.5
Solution
r = {-7.5, 5.5}

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