(z-3)(z+2)=27-3

Solution for (z-3)(z+2)=27-3 equation:

Simplifying
(z + -3)(z + 2) = 27 + -3

Reorder the terms:
(-3 + z)(z + 2) = 27 + -3

Reorder the terms:
(-3 + z)(2 + z) = 27 + -3

Multiply (-3 + z) * (2 + z)
(-3(2 + z) + z(2 + z)) = 27 + -3
((2 * -3 + z * -3) + z(2 + z)) = 27 + -3
((-6 + -3z) + z(2 + z)) = 27 + -3
(-6 + -3z + (2 * z + z * z)) = 27 + -3
(-6 + -3z + (2z + z2)) = 27 + -3

Combine like terms: -3z + 2z = -1z
(-6 + -1z + z2) = 27 + -3

Combine like terms: 27 + -3 = 24
-6 + -1z + z2 = 24

Solving
-6 + -1z + z2 = 24

Solving for variable 'z'.

Reorder the terms:
-6 + -24 + -1z + z2 = 24 + -24

Combine like terms: -6 + -24 = -30
-30 + -1z + z2 = 24 + -24

Combine like terms: 24 + -24 = 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}