2z+36=(2z+6)(z+2)

Solution for 2z+36=(2z+6)(z+2) equation:

Simplifying
2z + 36 = (2z + 6)(z + 2)

Reorder the terms:
36 + 2z = (2z + 6)(z + 2)

Reorder the terms:
36 + 2z = (6 + 2z)(z + 2)

Reorder the terms:
36 + 2z = (6 + 2z)(2 + z)

Multiply (6 + 2z) * (2 + z)
36 + 2z = (6(2 + z) + 2z * (2 + z))
36 + 2z = ((2 * 6 + z * 6) + 2z * (2 + z))
36 + 2z = ((12 + 6z) + 2z * (2 + z))
36 + 2z = (12 + 6z + (2 * 2z + z * 2z))
36 + 2z = (12 + 6z + (4z + 2z2))

Combine like terms: 6z + 4z = 10z
36 + 2z = (12 + 10z + 2z2)

Solving
36 + 2z = 12 + 10z + 2z2

Solving for variable 'z'.

Reorder the terms:
36 + -12 + 2z + -10z + -2z2 = 12 + 10z + 2z2 + -12 + -10z + -2z2

Combine like terms: 36 + -12 = 24
24 + 2z + -10z + -2z2 = 12 + 10z + 2z2 + -12 + -10z + -2z2

Combine like terms: 2z + -10z = -8z
24 + -8z + -2z2 = 12 + 10z + 2z2 + -12 + -10z + -2z2

Reorder the terms:
24 + -8z + -2z2 = 12 + -12 + 10z + -10z + 2z2 + -2z2

Combine like terms: 12 + -12 = 0
24 + -8z + -2z2 = 0 + 10z + -10z + 2z2 + -2z2
24 + -8z + -2z2 = 10z + -10z + 2z2 + -2z2

Combine like terms: 10z + -10z = 0
24 + -8z + -2z2 = 0 + 2z2 + -2z2
24 + -8z + -2z2 = 2z2 + -2z2

Combine like terms: 2z2 + -2z2 = 0
24 + -8z + -2z2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(12 + -4z + -1z2) = 0

Factor a trinomial.
2((2 + -1z)(6 + z)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(6 + z)' equal to zero and attempt to solve:

Simplifying
6 + z = 0

Solving
6 + z = 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 + z = 0 + -6

Combine like terms: 6 + -6 = 0
0 + z = 0 + -6
z = 0 + -6

Combine like terms: 0 + -6 = -6
z = -6

Simplifying
z = -6
Solution
z = {2, -6}