(f+6)(f+6)=144

Solution for (f+6)(f+6)=144 equation:

Simplifying
(f + 6)(f + 6) = 144

Reorder the terms:
(6 + f)(f + 6) = 144

Reorder the terms:
(6 + f)(6 + f) = 144

Multiply (6 + f) * (6 + f)
(6(6 + f) + f(6 + f)) = 144
((6 * 6 + f * 6) + f(6 + f)) = 144
((36 + 6f) + f(6 + f)) = 144
(36 + 6f + (6 * f + f * f)) = 144
(36 + 6f + (6f + f2)) = 144

Combine like terms: 6f + 6f = 12f
(36 + 12f + f2) = 144

Solving
36 + 12f + f2 = 144

Solving for variable 'f'.

Reorder the terms:
36 + -144 + 12f + f2 = 144 + -144

Combine like terms: 36 + -144 = -108
-108 + 12f + f2 = 144 + -144

Combine like terms: 144 + -144 = 0
-108 + 12f + f2 = 0

Factor a trinomial.
(-18 + -1f)(6 + -1f) = 0

Subproblem 1
Set the factor '(-18 + -1f)' equal to zero and attempt to solve:

Simplifying
-18 + -1f = 0

Solving
-18 + -1f = 0

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

Add '18' to each side of the equation.
-18 + 18 + -1f = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -1f = 0 + 18
-1f = 0 + 18

Combine like terms: 0 + 18 = 18
-1f = 18

Divide each side by '-1'.
f = -18

Simplifying
f = -18
Subproblem 2
Set the factor '(6 + -1f)' equal to zero and attempt to solve:

Simplifying
6 + -1f = 0

Solving
6 + -1f = 0

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

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

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

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

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

Simplifying
f = 6
Solution
f = {-18, 6}