(z-15)(z+21)=0

Solution for (z-15)(z+21)=0 equation:

Simplifying
(z + -15)(z + 21) = 0

Reorder the terms:
(-15 + z)(z + 21) = 0

Reorder the terms:
(-15 + z)(21 + z) = 0

Multiply (-15 + z) * (21 + z)
(-15(21 + z) + z(21 + z)) = 0
((21 * -15 + z * -15) + z(21 + z)) = 0
((-315 + -15z) + z(21 + z)) = 0
(-315 + -15z + (21 * z + z * z)) = 0
(-315 + -15z + (21z + z2)) = 0

Combine like terms: -15z + 21z = 6z
(-315 + 6z + z2) = 0

Solving
-315 + 6z + z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-21 + -1z)(15 + -1z) = 0

Subproblem 1
Set the factor '(-21 + -1z)' equal to zero and attempt to solve:

Simplifying
-21 + -1z = 0

Solving
-21 + -1z = 0

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

Add '21' to each side of the equation.
-21 + 21 + -1z = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -1z = 0 + 21
-1z = 0 + 21

Combine like terms: 0 + 21 = 21
-1z = 21

Divide each side by '-1'.
z = -21

Simplifying
z = -21
Subproblem 2
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
Solution
z = {-21, 15}