(z-8)(z+4)=-35

Solution for (z-8)(z+4)=-35 equation:

Simplifying
(z + -8)(z + 4) = -35

Reorder the terms:
(-8 + z)(z + 4) = -35

Reorder the terms:
(-8 + z)(4 + z) = -35

Multiply (-8 + z) * (4 + z)
(-8(4 + z) + z(4 + z)) = -35
((4 * -8 + z * -8) + z(4 + z)) = -35
((-32 + -8z) + z(4 + z)) = -35
(-32 + -8z + (4 * z + z * z)) = -35
(-32 + -8z + (4z + z2)) = -35

Combine like terms: -8z + 4z = -4z
(-32 + -4z + z2) = -35

Solving
-32 + -4z + z2 = -35

Solving for variable 'z'.

Reorder the terms:
-32 + 35 + -4z + z2 = -35 + 35

Combine like terms: -32 + 35 = 3
3 + -4z + z2 = -35 + 35

Combine like terms: -35 + 35 = 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}