2z+4=(2z+2)(z+2)

Solution for 2z+4=(2z+2)(z+2) equation:

Simplifying
2z + 4 = (2z + 2)(z + 2)

Reorder the terms:
4 + 2z = (2z + 2)(z + 2)

Reorder the terms:
4 + 2z = (2 + 2z)(z + 2)

Reorder the terms:
4 + 2z = (2 + 2z)(2 + z)

Multiply (2 + 2z) * (2 + z)
4 + 2z = (2(2 + z) + 2z * (2 + z))
4 + 2z = ((2 * 2 + z * 2) + 2z * (2 + z))
4 + 2z = ((4 + 2z) + 2z * (2 + z))
4 + 2z = (4 + 2z + (2 * 2z + z * 2z))
4 + 2z = (4 + 2z + (4z + 2z2))

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

Add '-4' to each side of the equation.
4 + -4 + 2z = 4 + 6z + -4 + 2z2

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

Reorder the terms:
2z = 4 + -4 + 6z + 2z2

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

Solving
2z = 6z + 2z2

Solving for variable 'z'.

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

Reorder the terms:
-4z + -2z2 = 6z + -6z + 2z2 + -2z2

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

Combine like terms: 2z2 + -2z2 = 0
-4z + -2z2 = 0

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

Ignore the factor -2.
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}