54=a*(a+3)

Solution for 54=a*(a+3) equation:

Simplifying
54 = a(a + 3)

Reorder the terms:
54 = a(3 + a)
54 = (3 * a + a * a)
54 = (3a + a2)

Solving
54 = 3a + a2

Solving for variable 'a'.

Reorder the terms:
54 + -3a + -1a2 = 3a + -3a + a2 + -1a2

Combine like terms: 3a + -3a = 0
54 + -3a + -1a2 = 0 + a2 + -1a2
54 + -3a + -1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
54 + -3a + -1a2 = 0

Factor a trinomial.
(6 + -1a)(9 + a) = 0

Subproblem 1
Set the factor '(6 + -1a)' equal to zero and attempt to solve:

Simplifying
6 + -1a = 0

Solving
6 + -1a = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1a = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1a = 0 + -6
-1a = 0 + -6

Combine like terms: 0 + -6 = -6
-1a = -6

Divide each side by '-1'.
a = 6

Simplifying
a = 6
Subproblem 2
Set the factor '(9 + a)' equal to zero and attempt to solve:

Simplifying
9 + a = 0

Solving
9 + a = 0

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

Add '-9' to each side of the equation.
9 + -9 + a = 0 + -9

Combine like terms: 9 + -9 = 0
0 + a = 0 + -9
a = 0 + -9

Combine like terms: 0 + -9 = -9
a = -9

Simplifying
a = -9
Solution
a = {6, -9}