2a^2+4a=5+a^2

Solution for 2a^2+4a=5+a^2 equation:

Simplifying
2a2 + 4a = 5 + a2

Reorder the terms:
4a + 2a2 = 5 + a2

Solving
4a + 2a2 = 5 + a2

Solving for variable 'a'.

Reorder the terms:
-5 + 4a + 2a2 + -1a2 = 5 + a2 + -5 + -1a2

Combine like terms: 2a2 + -1a2 = 1a2
-5 + 4a + 1a2 = 5 + a2 + -5 + -1a2

Reorder the terms:
-5 + 4a + 1a2 = 5 + -5 + a2 + -1a2

Combine like terms: 5 + -5 = 0
-5 + 4a + 1a2 = 0 + a2 + -1a2
-5 + 4a + 1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
-5 + 4a + 1a2 = 0

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