(z-9)(z+5)=-48

Solution for (z-9)(z+5)=-48 equation:

Simplifying
(z + -9)(z + 5) = -48

Reorder the terms:
(-9 + z)(z + 5) = -48

Reorder the terms:
(-9 + z)(5 + z) = -48

Multiply (-9 + z) * (5 + z)
(-9(5 + z) + z(5 + z)) = -48
((5 * -9 + z * -9) + z(5 + z)) = -48
((-45 + -9z) + z(5 + z)) = -48
(-45 + -9z + (5 * z + z * z)) = -48
(-45 + -9z + (5z + z2)) = -48

Combine like terms: -9z + 5z = -4z
(-45 + -4z + z2) = -48

Solving
-45 + -4z + z2 = -48

Solving for variable 'z'.

Reorder the terms:
-45 + 48 + -4z + z2 = -48 + 48

Combine like terms: -45 + 48 = 3
3 + -4z + z2 = -48 + 48

Combine like terms: -48 + 48 = 0
3 + -4z + z2 = 0

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

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

Simplifying
1 + -1z = 0

Solving
1 + -1z = 0

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

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

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

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

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

Simplifying
z = 1
Subproblem 2
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
Solution
z = {1, 3}