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

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

Simplifying
(2z + 6)(z + -2) = 0

Reorder the terms:
(6 + 2z)(z + -2) = 0

Reorder the terms:
(6 + 2z)(-2 + z) = 0

Multiply (6 + 2z) * (-2 + z)
(6(-2 + z) + 2z * (-2 + z)) = 0
((-2 * 6 + z * 6) + 2z * (-2 + z)) = 0
((-12 + 6z) + 2z * (-2 + z)) = 0
(-12 + 6z + (-2 * 2z + z * 2z)) = 0
(-12 + 6z + (-4z + 2z2)) = 0

Combine like terms: 6z + -4z = 2z
(-12 + 2z + 2z2) = 0

Solving
-12 + 2z + 2z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + z + z2) = 0

Factor a trinomial.
2((-3 + -1z)(2 + -1z)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(2 + -1z)' equal to zero and attempt to solve:

Simplifying
2 + -1z = 0

Solving
2 + -1z = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1z = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1z = 0 + -2
-1z = 0 + -2

Combine like terms: 0 + -2 = -2
-1z = -2

Divide each side by '-1'.
z = 2

Simplifying
z = 2
Solution
z = {-3, 2}