(a^2)+(70-10a)+(160-5a)=180

Solution for (a^2)+(70-10a)+(160-5a)=180 equation:

Simplifying
(a2) + (70 + -10a) + (160 + -5a) = 180
a2 + (70 + -10a) + (160 + -5a) = 180

Remove parenthesis around (70 + -10a)
a2 + 70 + -10a + (160 + -5a) = 180

Remove parenthesis around (160 + -5a)
a2 + 70 + -10a + 160 + -5a = 180

Reorder the terms:
70 + 160 + -10a + -5a + a2 = 180

Combine like terms: 70 + 160 = 230
230 + -10a + -5a + a2 = 180

Combine like terms: -10a + -5a = -15a
230 + -15a + a2 = 180

Solving
230 + -15a + a2 = 180

Solving for variable 'a'.

Reorder the terms:
230 + -180 + -15a + a2 = 180 + -180

Combine like terms: 230 + -180 = 50
50 + -15a + a2 = 180 + -180

Combine like terms: 180 + -180 = 0
50 + -15a + a2 = 0

Factor a trinomial.
(5 + -1a)(10 + -1a) = 0

Subproblem 1
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
Subproblem 2
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
Solution
a = {5, 10}