8=a(a+2)

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

Simplifying
8 = a(a + 2)

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

Solving
8 = 2a + a2

Solving for variable 'a'.

Reorder the terms:
8 + -2a + -1a2 = 2a + -2a + a2 + -1a2

Combine like terms: 2a + -2a = 0
8 + -2a + -1a2 = 0 + a2 + -1a2
8 + -2a + -1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
8 + -2a + -1a2 = 0

Factor a trinomial.
(2 + -1a)(4 + a) = 0

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

Simplifying
2 + -1a = 0

Solving
2 + -1a = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1a = 0 + -2
-1a = 0 + -2

Combine like terms: 0 + -2 = -2
-1a = -2

Divide each side by '-1'.
a = 2

Simplifying
a = 2
Subproblem 2
Set the factor '(4 + a)' equal to zero and attempt to solve:

Simplifying
4 + a = 0

Solving
4 + a = 0

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

Add '-4' to each side of the equation.
4 + -4 + a = 0 + -4

Combine like terms: 4 + -4 = 0
0 + a = 0 + -4
a = 0 + -4

Combine like terms: 0 + -4 = -4
a = -4

Simplifying
a = -4
Solution
a = {2, -4}