(f-12)(f-12)=25

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Solution for (f-12)(f-12)=25 equation: 


Simplifying
(f + -12)(f + -12) = 25

Reorder the terms:
(-12 + f)(f + -12) = 25

Reorder the terms:
(-12 + f)(-12 + f) = 25

Multiply (-12 + f) * (-12 + f)
(-12(-12 + f) + f(-12 + f)) = 25
((-12 * -12 + f * -12) + f(-12 + f)) = 25
((144 + -12f) + f(-12 + f)) = 25
(144 + -12f + (-12 * f + f * f)) = 25
(144 + -12f + (-12f + f2)) = 25

Combine like terms: -12f + -12f = -24f
(144 + -24f + f2) = 25

Solving
144 + -24f + f2 = 25

Solving for variable 'f'.

Reorder the terms:
144 + -25 + -24f + f2 = 25 + -25

Combine like terms: 144 + -25 = 119
119 + -24f + f2 = 25 + -25

Combine like terms: 25 + -25 = 0
119 + -24f + f2 = 0

Factor a trinomial.
(7 + -1f)(17 + -1f) = 0


Subproblem 1
Set the factor '(7 + -1f)' equal to zero and attempt to solve:

Simplifying
7 + -1f = 0

Solving
7 + -1f = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1f = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1f = 0 + -7
-1f = 0 + -7

Combine like terms: 0 + -7 = -7
-1f = -7

Divide each side by '-1'.
f = 7

Simplifying
f = 7

Subproblem 2
Set the factor '(17 + -1f)' equal to zero and attempt to solve:

Simplifying
17 + -1f = 0

Solving
17 + -1f = 0

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

Add '-17' to each side of the equation.
17 + -17 + -1f = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -1f = 0 + -17
-1f = 0 + -17

Combine like terms: 0 + -17 = -17
-1f = -17

Divide each side by '-1'.
f = 17

Simplifying
f = 17
Solution
f = {7, 17}

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