(z-7)(z+3)=-24

Solution for (z-7)(z+3)=-24 equation:

Simplifying
(z + -7)(z + 3) = -24

Reorder the terms:
(-7 + z)(z + 3) = -24

Reorder the terms:
(-7 + z)(3 + z) = -24

Multiply (-7 + z) * (3 + z)
(-7(3 + z) + z(3 + z)) = -24
((3 * -7 + z * -7) + z(3 + z)) = -24
((-21 + -7z) + z(3 + z)) = -24
(-21 + -7z + (3 * z + z * z)) = -24
(-21 + -7z + (3z + z2)) = -24

Combine like terms: -7z + 3z = -4z
(-21 + -4z + z2) = -24

Solving
-21 + -4z + z2 = -24

Solving for variable 'z'.

Reorder the terms:
-21 + 24 + -4z + z2 = -24 + 24

Combine like terms: -21 + 24 = 3
3 + -4z + z2 = -24 + 24

Combine like terms: -24 + 24 = 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}