[a*(a+2)]=3*5

Solution for [a*(a+2)]=3*5 equation:

Simplifying
[a(a + 2)] = 3 * 5

Reorder the terms:
[a(2 + a)] = 3 * 5
[(2 * a + a * a)] = 3 * 5
[(2a + a2)] = 3 * 5
[2a + a2] = 3 * 5

Remove brackets around [2a + a2]
2a + a2 = 3 * 5

Multiply 3 * 5
2a + a2 = 15

Solving
2a + a2 = 15

Solving for variable 'a'.

Reorder the terms:
-15 + 2a + a2 = 15 + -15

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

Factor a trinomial.
(-5 + -1a)(3 + -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 '(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
Solution
a = {-5, 3}