(z-5)(z+4)=90

Solution for (z-5)(z+4)=90 equation:

Simplifying
(z + -5)(z + 4) = 90

Reorder the terms:
(-5 + z)(z + 4) = 90

Reorder the terms:
(-5 + z)(4 + z) = 90

Multiply (-5 + z) * (4 + z)
(-5(4 + z) + z(4 + z)) = 90
((4 * -5 + z * -5) + z(4 + z)) = 90
((-20 + -5z) + z(4 + z)) = 90
(-20 + -5z + (4 * z + z * z)) = 90
(-20 + -5z + (4z + z2)) = 90

Combine like terms: -5z + 4z = -1z
(-20 + -1z + z2) = 90

Solving
-20 + -1z + z2 = 90

Solving for variable 'z'.

Reorder the terms:
-20 + -90 + -1z + z2 = 90 + -90

Combine like terms: -20 + -90 = -110
-110 + -1z + z2 = 90 + -90

Combine like terms: 90 + -90 = 0
-110 + -1z + z2 = 0

Factor a trinomial.
(-10 + -1z)(11 + -1z) = 0

Subproblem 1
Set the factor '(-10 + -1z)' equal to zero and attempt to solve:

Simplifying
-10 + -1z = 0

Solving
-10 + -1z = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1z = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1z = 0 + 10
-1z = 0 + 10

Combine like terms: 0 + 10 = 10
-1z = 10

Divide each side by '-1'.
z = -10

Simplifying
z = -10
Subproblem 2
Set the factor '(11 + -1z)' equal to zero and attempt to solve:

Simplifying
11 + -1z = 0

Solving
11 + -1z = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1z = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1z = 0 + -11
-1z = 0 + -11

Combine like terms: 0 + -11 = -11
-1z = -11

Divide each side by '-1'.
z = 11

Simplifying
z = 11
Solution
z = {-10, 11}