(z-6)(z+2)=-15

Solution for (z-6)(z+2)=-15 equation:

Simplifying
(z + -6)(z + 2) = -15

Reorder the terms:
(-6 + z)(z + 2) = -15

Reorder the terms:
(-6 + z)(2 + z) = -15

Multiply (-6 + z) * (2 + z)
(-6(2 + z) + z(2 + z)) = -15
((2 * -6 + z * -6) + z(2 + z)) = -15
((-12 + -6z) + z(2 + z)) = -15
(-12 + -6z + (2 * z + z * z)) = -15
(-12 + -6z + (2z + z2)) = -15

Combine like terms: -6z + 2z = -4z
(-12 + -4z + z2) = -15

Solving
-12 + -4z + z2 = -15

Solving for variable 'z'.

Reorder the terms:
-12 + 15 + -4z + z2 = -15 + 15

Combine like terms: -12 + 15 = 3
3 + -4z + z2 = -15 + 15

Combine like terms: -15 + 15 = 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}