21=a(a+4)

Solution for 21=a(a+4) equation:

Simplifying
21 = a(a + 4)

Reorder the terms:
21 = a(4 + a)
21 = (4 * a + a * a)
21 = (4a + a2)

Solving
21 = 4a + a2

Solving for variable 'a'.

Reorder the terms:
21 + -4a + -1a2 = 4a + -4a + a2 + -1a2

Combine like terms: 4a + -4a = 0
21 + -4a + -1a2 = 0 + a2 + -1a2
21 + -4a + -1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
21 + -4a + -1a2 = 0

Factor a trinomial.
(3 + -1a)(7 + a) = 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 '(7 + a)' equal to zero and attempt to solve:

Simplifying
7 + a = 0

Solving
7 + a = 0

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

Add '-7' to each side of the equation.
7 + -7 + a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + a = 0 + -7
a = 0 + -7

Combine like terms: 0 + -7 = -7
a = -7

Simplifying
a = -7
Solution
a = {3, -7}