(z-2)(z+9)=

Solution for (z-2)(z+9)= equation:

Simplifying
(z + -2)(z + 9) = 0

Reorder the terms:
(-2 + z)(z + 9) = 0

Reorder the terms:
(-2 + z)(9 + z) = 0

Multiply (-2 + z) * (9 + z)
(-2(9 + z) + z(9 + z)) = 0
((9 * -2 + z * -2) + z(9 + z)) = 0
((-18 + -2z) + z(9 + z)) = 0
(-18 + -2z + (9 * z + z * z)) = 0
(-18 + -2z + (9z + z2)) = 0

Combine like terms: -2z + 9z = 7z
(-18 + 7z + z2) = 0

Solving
-18 + 7z + z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-9 + -1z)(2 + -1z) = 0

Subproblem 1
Set the factor '(-9 + -1z)' equal to zero and attempt to solve:

Simplifying
-9 + -1z = 0

Solving
-9 + -1z = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1z = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1z = 0 + 9
-1z = 0 + 9

Combine like terms: 0 + 9 = 9
-1z = 9

Divide each side by '-1'.
z = -9

Simplifying
z = -9
Subproblem 2
Set the factor '(2 + -1z)' equal to zero and attempt to solve:

Simplifying
2 + -1z = 0

Solving
2 + -1z = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1z = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1z = 0 + -2
-1z = 0 + -2

Combine like terms: 0 + -2 = -2
-1z = -2

Divide each side by '-1'.
z = 2

Simplifying
z = 2
Solution
z = {-9, 2}