(z-9)(z+2)=

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

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

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

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

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

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

Solving
-18 + -7z + z2 = 0

Solving for variable 'z'.

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

Subproblem 1
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
Subproblem 2
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
Solution
z = {-2, 9}