(z+2)(z+2)+8=6z+12

Solution for (z+2)(z+2)+8=6z+12 equation:

Simplifying
(z + 2)(z + 2) + 8 = 6z + 12

Reorder the terms:
(2 + z)(z + 2) + 8 = 6z + 12

Reorder the terms:
(2 + z)(2 + z) + 8 = 6z + 12

Multiply (2 + z) * (2 + z)
(2(2 + z) + z(2 + z)) + 8 = 6z + 12
((2 * 2 + z * 2) + z(2 + z)) + 8 = 6z + 12
((4 + 2z) + z(2 + z)) + 8 = 6z + 12
(4 + 2z + (2 * z + z * z)) + 8 = 6z + 12
(4 + 2z + (2z + z2)) + 8 = 6z + 12

Combine like terms: 2z + 2z = 4z
(4 + 4z + z2) + 8 = 6z + 12

Reorder the terms:
4 + 8 + 4z + z2 = 6z + 12

Combine like terms: 4 + 8 = 12
12 + 4z + z2 = 6z + 12

Reorder the terms:
12 + 4z + z2 = 12 + 6z

Add '-12' to each side of the equation.
12 + 4z + -12 + z2 = 12 + -12 + 6z

Reorder the terms:
12 + -12 + 4z + z2 = 12 + -12 + 6z

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

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

Solving
4z + z2 = 6z

Solving for variable 'z'.

Reorder the terms:
4z + -6z + z2 = 6z + -6z

Combine like terms: 4z + -6z = -2z
-2z + z2 = 6z + -6z

Combine like terms: 6z + -6z = 0
-2z + z2 = 0

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

Subproblem 1
Set the factor 'z' equal to zero and attempt to solve:

Simplifying
z = 0

Solving
z = 0

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

Simplifying
z = 0
Subproblem 2
Set the factor '(-2 + z)' equal to zero and attempt to solve:

Simplifying
-2 + z = 0

Solving
-2 + z = 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 + z = 0 + 2

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

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

Simplifying
z = 2
Solution
z = {0, 2}