(z-5)(z+4)=10

Solution for (z-5)(z+4)=10 equation:

Simplifying
(z + -5)(z + 4) = 10

Reorder the terms:
(-5 + z)(z + 4) = 10

Reorder the terms:
(-5 + z)(4 + z) = 10

Multiply (-5 + z) * (4 + z)
(-5(4 + z) + z(4 + z)) = 10
((4 * -5 + z * -5) + z(4 + z)) = 10
((-20 + -5z) + z(4 + z)) = 10
(-20 + -5z + (4 * z + z * z)) = 10
(-20 + -5z + (4z + z2)) = 10

Combine like terms: -5z + 4z = -1z
(-20 + -1z + z2) = 10

Solving
-20 + -1z + z2 = 10

Solving for variable 'z'.

Reorder the terms:
-20 + -10 + -1z + z2 = 10 + -10

Combine like terms: -20 + -10 = -30
-30 + -1z + z2 = 10 + -10

Combine like terms: 10 + -10 = 0
-30 + -1z + z2 = 0

Factor a trinomial.
(-5 + -1z)(6 + -1z) = 0

Subproblem 1
Set the factor '(-5 + -1z)' equal to zero and attempt to solve:

Simplifying
-5 + -1z = 0

Solving
-5 + -1z = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1z = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1z = 0 + 5
-1z = 0 + 5

Combine like terms: 0 + 5 = 5
-1z = 5

Divide each side by '-1'.
z = -5

Simplifying
z = -5
Subproblem 2
Set the factor '(6 + -1z)' equal to zero and attempt to solve:

Simplifying
6 + -1z = 0

Solving
6 + -1z = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1z = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1z = 0 + -6
-1z = 0 + -6

Combine like terms: 0 + -6 = -6
-1z = -6

Divide each side by '-1'.
z = 6

Simplifying
z = 6
Solution
z = {-5, 6}