(a+7)(a-5)=

Solution for (a+7)(a-5)= equation:

Simplifying
(a + 7)(a + -5) = 0

Reorder the terms:
(7 + a)(a + -5) = 0

Reorder the terms:
(7 + a)(-5 + a) = 0

Multiply (7 + a) * (-5 + a)
(7(-5 + a) + a(-5 + a)) = 0
((-5 * 7 + a * 7) + a(-5 + a)) = 0
((-35 + 7a) + a(-5 + a)) = 0
(-35 + 7a + (-5 * a + a * a)) = 0
(-35 + 7a + (-5a + a2)) = 0

Combine like terms: 7a + -5a = 2a
(-35 + 2a + a2) = 0

Solving
-35 + 2a + a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-7 + -1a)(5 + -1a) = 0

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

Simplifying
-7 + -1a = 0

Solving
-7 + -1a = 0

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

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

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

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

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

Simplifying
a = -7
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 = {-7, 5}