(f-5)(f+1)=(f+3)(f+7)

Solution for (f-5)(f+1)=(f+3)(f+7) equation:

Simplifying
(f + -5)(f + 1) = (f + 3)(f + 7)

Reorder the terms:
(-5 + f)(f + 1) = (f + 3)(f + 7)

Reorder the terms:
(-5 + f)(1 + f) = (f + 3)(f + 7)

Multiply (-5 + f) * (1 + f)
(-5(1 + f) + f(1 + f)) = (f + 3)(f + 7)
((1 * -5 + f * -5) + f(1 + f)) = (f + 3)(f + 7)
((-5 + -5f) + f(1 + f)) = (f + 3)(f + 7)
(-5 + -5f + (1 * f + f * f)) = (f + 3)(f + 7)
(-5 + -5f + (1f + f2)) = (f + 3)(f + 7)

Combine like terms: -5f + 1f = -4f
(-5 + -4f + f2) = (f + 3)(f + 7)

Reorder the terms:
-5 + -4f + f2 = (3 + f)(f + 7)

Reorder the terms:
-5 + -4f + f2 = (3 + f)(7 + f)

Multiply (3 + f) * (7 + f)
-5 + -4f + f2 = (3(7 + f) + f(7 + f))
-5 + -4f + f2 = ((7 * 3 + f * 3) + f(7 + f))
-5 + -4f + f2 = ((21 + 3f) + f(7 + f))
-5 + -4f + f2 = (21 + 3f + (7 * f + f * f))
-5 + -4f + f2 = (21 + 3f + (7f + f2))

Combine like terms: 3f + 7f = 10f
-5 + -4f + f2 = (21 + 10f + f2)

Add '-1f2' to each side of the equation.
-5 + -4f + f2 + -1f2 = 21 + 10f + f2 + -1f2

Combine like terms: f2 + -1f2 = 0
-5 + -4f + 0 = 21 + 10f + f2 + -1f2
-5 + -4f = 21 + 10f + f2 + -1f2

Combine like terms: f2 + -1f2 = 0
-5 + -4f = 21 + 10f + 0
-5 + -4f = 21 + 10f

Solving
-5 + -4f = 21 + 10f

Solving for variable 'f'.

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

Add '-10f' to each side of the equation.
-5 + -4f + -10f = 21 + 10f + -10f

Combine like terms: -4f + -10f = -14f
-5 + -14f = 21 + 10f + -10f

Combine like terms: 10f + -10f = 0
-5 + -14f = 21 + 0
-5 + -14f = 21

Add '5' to each side of the equation.
-5 + 5 + -14f = 21 + 5

Combine like terms: -5 + 5 = 0
0 + -14f = 21 + 5
-14f = 21 + 5

Combine like terms: 21 + 5 = 26
-14f = 26

Divide each side by '-14'.
f = -1.857142857

Simplifying
f = -1.857142857