a(a+3)=18-2(3-2a)

Solution for a(a+3)=18-2(3-2a) equation:

Simplifying
a(a + 3) = 18 + -2(3 + -2a)

Reorder the terms:
a(3 + a) = 18 + -2(3 + -2a)
(3 * a + a * a) = 18 + -2(3 + -2a)
(3a + a2) = 18 + -2(3 + -2a)
3a + a2 = 18 + (3 * -2 + -2a * -2)
3a + a2 = 18 + (-6 + 4a)

Combine like terms: 18 + -6 = 12
3a + a2 = 12 + 4a

Solving
3a + a2 = 12 + 4a

Solving for variable 'a'.

Reorder the terms:
-12 + 3a + -4a + a2 = 12 + 4a + -12 + -4a

Combine like terms: 3a + -4a = -1a
-12 + -1a + a2 = 12 + 4a + -12 + -4a

Reorder the terms:
-12 + -1a + a2 = 12 + -12 + 4a + -4a

Combine like terms: 12 + -12 = 0
-12 + -1a + a2 = 0 + 4a + -4a
-12 + -1a + a2 = 4a + -4a

Combine like terms: 4a + -4a = 0
-12 + -1a + a2 = 0

Factor a trinomial.
(-3 + -1a)(4 + -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 '(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 = {-3, 4}