15(a+8)+15a=2a(a+8)

Solution for 15(a+8)+15a=2a(a+8) equation:

Simplifying
15(a + 8) + 15a = 2a(a + 8)

Reorder the terms:
15(8 + a) + 15a = 2a(a + 8)
(8 * 15 + a * 15) + 15a = 2a(a + 8)
(120 + 15a) + 15a = 2a(a + 8)

Combine like terms: 15a + 15a = 30a
120 + 30a = 2a(a + 8)

Reorder the terms:
120 + 30a = 2a(8 + a)
120 + 30a = (8 * 2a + a * 2a)
120 + 30a = (16a + 2a2)

Solving
120 + 30a = 16a + 2a2

Solving for variable 'a'.

Combine like terms: 30a + -16a = 14a
120 + 14a + -2a2 = 16a + 2a2 + -16a + -2a2

Reorder the terms:
120 + 14a + -2a2 = 16a + -16a + 2a2 + -2a2

Combine like terms: 16a + -16a = 0
120 + 14a + -2a2 = 0 + 2a2 + -2a2
120 + 14a + -2a2 = 2a2 + -2a2

Combine like terms: 2a2 + -2a2 = 0
120 + 14a + -2a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(60 + 7a + -1a2) = 0

Factor a trinomial.
2((12 + -1a)(5 + a)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(5 + a)' equal to zero and attempt to solve:

Simplifying
5 + a = 0

Solving
5 + a = 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 + a = 0 + -5

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

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

Simplifying
a = -5
Solution
a = {12, -5}