2a(a+1)=a^2+3

Solution for 2a(a+1)=a^2+3 equation:

Simplifying
2a(a + 1) = a2 + 3

Reorder the terms:
2a(1 + a) = a2 + 3
(1 * 2a + a * 2a) = a2 + 3
(2a + 2a2) = a2 + 3

Reorder the terms:
2a + 2a2 = 3 + a2

Solving
2a + 2a2 = 3 + a2

Solving for variable 'a'.

Reorder the terms:
-3 + 2a + 2a2 + -1a2 = 3 + a2 + -3 + -1a2

Combine like terms: 2a2 + -1a2 = 1a2
-3 + 2a + 1a2 = 3 + a2 + -3 + -1a2

Reorder the terms:
-3 + 2a + 1a2 = 3 + -3 + a2 + -1a2

Combine like terms: 3 + -3 = 0
-3 + 2a + 1a2 = 0 + a2 + -1a2
-3 + 2a + 1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
-3 + 2a + 1a2 = 0

Factor a trinomial.
(-3 + -1a)(1 + -1a) = 0

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

Simplifying
1 + -1a = 0

Solving
1 + -1a = 0

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

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

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

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

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

Simplifying
a = 1
Solution
a = {-3, 1}