2a(a+1)=a^2+8

Solution for 2a(a+1)=a^2+8 equation:

Simplifying
2a(a + 1) = a2 + 8

Reorder the terms:
2a(1 + a) = a2 + 8
(1 * 2a + a * 2a) = a2 + 8
(2a + 2a2) = a2 + 8

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

Solving
2a + 2a2 = 8 + a2

Solving for variable 'a'.

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

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

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

Combine like terms: 8 + -8 = 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.
(-4 + -1a)(2 + -1a) = 0

Subproblem 1
Set the factor '(-4 + -1a)' equal to zero and attempt to solve:

Simplifying
-4 + -1a = 0

Solving
-4 + -1a = 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 + -1a = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1a = 0 + 4
-1a = 0 + 4

Combine like terms: 0 + 4 = 4
-1a = 4

Divide each side by '-1'.
a = -4

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