(a+-10)(a+-14)=0

Solution for (a+-10)(a+-14)=0 equation:

Simplifying
(a + -10)(a + -14) = 0

Reorder the terms:
(-10 + a)(a + -14) = 0

Reorder the terms:
(-10 + a)(-14 + a) = 0

Multiply (-10 + a) * (-14 + a)
(-10(-14 + a) + a(-14 + a)) = 0
((-14 * -10 + a * -10) + a(-14 + a)) = 0
((140 + -10a) + a(-14 + a)) = 0
(140 + -10a + (-14 * a + a * a)) = 0
(140 + -10a + (-14a + a2)) = 0

Combine like terms: -10a + -14a = -24a
(140 + -24a + a2) = 0

Solving
140 + -24a + a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(10 + -1a)(14 + -1a) = 0

Subproblem 1
Set the factor '(10 + -1a)' equal to zero and attempt to solve:

Simplifying
10 + -1a = 0

Solving
10 + -1a = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1a = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1a = 0 + -10
-1a = 0 + -10

Combine like terms: 0 + -10 = -10
-1a = -10

Divide each side by '-1'.
a = 10

Simplifying
a = 10
Subproblem 2
Set the factor '(14 + -1a)' equal to zero and attempt to solve:

Simplifying
14 + -1a = 0

Solving
14 + -1a = 0

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

Add '-14' to each side of the equation.
14 + -14 + -1a = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -1a = 0 + -14
-1a = 0 + -14

Combine like terms: 0 + -14 = -14
-1a = -14

Divide each side by '-1'.
a = 14

Simplifying
a = 14
Solution
a = {10, 14}