(a+2)(a-4)=7

Solution for (a+2)(a-4)=7 equation:

Simplifying
(a + 2)(a + -4) = 7

Reorder the terms:
(2 + a)(a + -4) = 7

Reorder the terms:
(2 + a)(-4 + a) = 7

Multiply (2 + a) * (-4 + a)
(2(-4 + a) + a(-4 + a)) = 7
((-4 * 2 + a * 2) + a(-4 + a)) = 7
((-8 + 2a) + a(-4 + a)) = 7
(-8 + 2a + (-4 * a + a * a)) = 7
(-8 + 2a + (-4a + a2)) = 7

Combine like terms: 2a + -4a = -2a
(-8 + -2a + a2) = 7

Solving
-8 + -2a + a2 = 7

Solving for variable 'a'.

Reorder the terms:
-8 + -7 + -2a + a2 = 7 + -7

Combine like terms: -8 + -7 = -15
-15 + -2a + a2 = 7 + -7

Combine like terms: 7 + -7 = 0
-15 + -2a + a2 = 0

Factor a trinomial.
(-3 + -1a)(5 + -1a) = 0

Subproblem 1
Set the factor '(-3 + -1a)' equal to zero and attempt to solve:

Simplifying
-3 + -1a = 0

Solving
-3 + -1a = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1a = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1a = 0 + 3
-1a = 0 + 3

Combine like terms: 0 + 3 = 3
-1a = 3

Divide each side by '-1'.
a = -3

Simplifying
a = -3
Subproblem 2
Set the factor '(5 + -1a)' equal to zero and attempt to solve:

Simplifying
5 + -1a = 0

Solving
5 + -1a = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1a = 0 + -5
-1a = 0 + -5

Combine like terms: 0 + -5 = -5
-1a = -5

Divide each side by '-1'.
a = 5

Simplifying
a = 5
Solution
a = {-3, 5}