4a+a=a(a+1)

Solution for 4a+a=a(a+1) equation:

Simplifying
4a + a = a(a + 1)

Combine like terms: 4a + a = 5a
5a = a(a + 1)

Reorder the terms:
5a = a(1 + a)
5a = (1 * a + a * a)
5a = (1a + a2)

Solving
5a = 1a + a2

Solving for variable 'a'.

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

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

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

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

Factor out the Greatest Common Factor (GCF), 'a'.
a(4 + -1a) = 0

Subproblem 1
Set the factor 'a' equal to zero and attempt to solve:

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0
Subproblem 2
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
Solution
a = {0, 4}