(a-4)(a-2)=80

Solution for (a-4)(a-2)=80 equation:

Simplifying
(a + -4)(a + -2) = 80

Reorder the terms:
(-4 + a)(a + -2) = 80

Reorder the terms:
(-4 + a)(-2 + a) = 80

Multiply (-4 + a) * (-2 + a)
(-4(-2 + a) + a(-2 + a)) = 80
((-2 * -4 + a * -4) + a(-2 + a)) = 80
((8 + -4a) + a(-2 + a)) = 80
(8 + -4a + (-2 * a + a * a)) = 80
(8 + -4a + (-2a + a2)) = 80

Combine like terms: -4a + -2a = -6a
(8 + -6a + a2) = 80

Solving
8 + -6a + a2 = 80

Solving for variable 'a'.

Reorder the terms:
8 + -80 + -6a + a2 = 80 + -80

Combine like terms: 8 + -80 = -72
-72 + -6a + a2 = 80 + -80

Combine like terms: 80 + -80 = 0
-72 + -6a + a2 = 0

Factor a trinomial.
(-6 + -1a)(12 + -1a) = 0

Subproblem 1
Set the factor '(-6 + -1a)' equal to zero and attempt to solve:

Simplifying
-6 + -1a = 0

Solving
-6 + -1a = 0

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

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

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

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

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

Simplifying
a = -6
Subproblem 2
Set the factor '(12 + -1a)' equal to zero and attempt to solve:

Simplifying
12 + -1a = 0

Solving
12 + -1a = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1a = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1a = 0 + -12
-1a = 0 + -12

Combine like terms: 0 + -12 = -12
-1a = -12

Divide each side by '-1'.
a = 12

Simplifying
a = 12
Solution
a = {-6, 12}