(f+1)(f-8)=0

Solution for (f+1)(f-8)=0 equation:

Simplifying
(f + 1)(f + -8) = 0

Reorder the terms:
(1 + f)(f + -8) = 0

Reorder the terms:
(1 + f)(-8 + f) = 0

Multiply (1 + f) * (-8 + f)
(1(-8 + f) + f(-8 + f)) = 0
((-8 * 1 + f * 1) + f(-8 + f)) = 0
((-8 + 1f) + f(-8 + f)) = 0
(-8 + 1f + (-8 * f + f * f)) = 0
(-8 + 1f + (-8f + f2)) = 0

Combine like terms: 1f + -8f = -7f
(-8 + -7f + f2) = 0

Solving
-8 + -7f + f2 = 0

Solving for variable 'f'.

Factor a trinomial.
(-1 + -1f)(8 + -1f) = 0

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

Simplifying
-1 + -1f = 0

Solving
-1 + -1f = 0

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

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

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

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

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

Simplifying
f = -1
Subproblem 2
Set the factor '(8 + -1f)' equal to zero and attempt to solve:

Simplifying
8 + -1f = 0

Solving
8 + -1f = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1f = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1f = 0 + -8
-1f = 0 + -8

Combine like terms: 0 + -8 = -8
-1f = -8

Divide each side by '-1'.
f = 8

Simplifying
f = 8
Solution
f = {-1, 8}