(z-5)(z+4)=52

Solution for (z-5)(z+4)=52 equation:

Simplifying
(z + -5)(z + 4) = 52

Reorder the terms:
(-5 + z)(z + 4) = 52

Reorder the terms:
(-5 + z)(4 + z) = 52

Multiply (-5 + z) * (4 + z)
(-5(4 + z) + z(4 + z)) = 52
((4 * -5 + z * -5) + z(4 + z)) = 52
((-20 + -5z) + z(4 + z)) = 52
(-20 + -5z + (4 * z + z * z)) = 52
(-20 + -5z + (4z + z2)) = 52

Combine like terms: -5z + 4z = -1z
(-20 + -1z + z2) = 52

Solving
-20 + -1z + z2 = 52

Solving for variable 'z'.

Reorder the terms:
-20 + -52 + -1z + z2 = 52 + -52

Combine like terms: -20 + -52 = -72
-72 + -1z + z2 = 52 + -52

Combine like terms: 52 + -52 = 0
-72 + -1z + z2 = 0

Factor a trinomial.
(-8 + -1z)(9 + -1z) = 0

Subproblem 1
Set the factor '(-8 + -1z)' equal to zero and attempt to solve:

Simplifying
-8 + -1z = 0

Solving
-8 + -1z = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1z = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1z = 0 + 8
-1z = 0 + 8

Combine like terms: 0 + 8 = 8
-1z = 8

Divide each side by '-1'.
z = -8

Simplifying
z = -8
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 = {-8, 9}