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

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

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

Reorder the terms:
z(-3 + z) + 2(z + 3) = 18
(-3 * z + z * z) + 2(z + 3) = 18
(-3z + z2) + 2(z + 3) = 18

Reorder the terms:
-3z + z2 + 2(3 + z) = 18
-3z + z2 + (3 * 2 + z * 2) = 18
-3z + z2 + (6 + 2z) = 18

Reorder the terms:
6 + -3z + 2z + z2 = 18

Combine like terms: -3z + 2z = -1z
6 + -1z + z2 = 18

Solving
6 + -1z + z2 = 18

Solving for variable 'z'.

Reorder the terms:
6 + -18 + -1z + z2 = 18 + -18

Combine like terms: 6 + -18 = -12
-12 + -1z + z2 = 18 + -18

Combine like terms: 18 + -18 = 0
-12 + -1z + z2 = 0

Factor a trinomial.
(-3 + -1z)(4 + -1z) = 0

Subproblem 1
Set the factor '(-3 + -1z)' equal to zero and attempt to solve:

Simplifying
-3 + -1z = 0

Solving
-3 + -1z = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1z = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1z = 0 + 3
-1z = 0 + 3

Combine like terms: 0 + 3 = 3
-1z = 3

Divide each side by '-1'.
z = -3

Simplifying
z = -3
Subproblem 2
Set the factor '(4 + -1z)' equal to zero and attempt to solve:

Simplifying
4 + -1z = 0

Solving
4 + -1z = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1z = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1z = 0 + -4
-1z = 0 + -4

Combine like terms: 0 + -4 = -4
-1z = -4

Divide each side by '-1'.
z = 4

Simplifying
z = 4
Solution
z = {-3, 4}