(z-18)(z-15)=0

Solution for (z-18)(z-15)=0 equation:

Simplifying
(z + -18)(z + -15) = 0

Reorder the terms:
(-18 + z)(z + -15) = 0

Reorder the terms:
(-18 + z)(-15 + z) = 0

Multiply (-18 + z) * (-15 + z)
(-18(-15 + z) + z(-15 + z)) = 0
((-15 * -18 + z * -18) + z(-15 + z)) = 0
((270 + -18z) + z(-15 + z)) = 0
(270 + -18z + (-15 * z + z * z)) = 0
(270 + -18z + (-15z + z2)) = 0

Combine like terms: -18z + -15z = -33z
(270 + -33z + z2) = 0

Solving
270 + -33z + z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(15 + -1z)(18 + -1z) = 0

Subproblem 1
Set the factor '(15 + -1z)' equal to zero and attempt to solve:

Simplifying
15 + -1z = 0

Solving
15 + -1z = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1z = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1z = 0 + -15
-1z = 0 + -15

Combine like terms: 0 + -15 = -15
-1z = -15

Divide each side by '-1'.
z = 15

Simplifying
z = 15
Subproblem 2
Set the factor '(18 + -1z)' equal to zero and attempt to solve:

Simplifying
18 + -1z = 0

Solving
18 + -1z = 0

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

Add '-18' to each side of the equation.
18 + -18 + -1z = 0 + -18

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

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

Divide each side by '-1'.
z = 18

Simplifying
z = 18
Solution
z = {15, 18}