4(4+12)=z(z+12)

Solution for 4(4+12)=z(z+12) equation:

Simplifying
4(4 + 12) = z(z + 12)

Combine like terms: 4 + 12 = 16
4(16) = z(z + 12)

Multiply 4 * 16
64 = z(z + 12)

Reorder the terms:
64 = z(12 + z)
64 = (12 * z + z * z)
64 = (12z + z2)

Solving
64 = 12z + z2

Solving for variable 'z'.

Reorder the terms:
64 + -12z + -1z2 = 12z + -12z + z2 + -1z2

Combine like terms: 12z + -12z = 0
64 + -12z + -1z2 = 0 + z2 + -1z2
64 + -12z + -1z2 = z2 + -1z2

Combine like terms: z2 + -1z2 = 0
64 + -12z + -1z2 = 0

Factor a trinomial.
(4 + -1z)(16 + z) = 0

Subproblem 1
Set the factor '(4 + -1z)' equal to zero and attempt to solve:

Simplifying
4 + -1z = 0

Solving
4 + -1z = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1z = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1z = 0 + -4
-1z = 0 + -4

Combine like terms: 0 + -4 = -4
-1z = -4

Divide each side by '-1'.
z = 4

Simplifying
z = 4
Subproblem 2
Set the factor '(16 + z)' equal to zero and attempt to solve:

Simplifying
16 + z = 0

Solving
16 + z = 0

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

Add '-16' to each side of the equation.
16 + -16 + z = 0 + -16

Combine like terms: 16 + -16 = 0
0 + z = 0 + -16
z = 0 + -16

Combine like terms: 0 + -16 = -16
z = -16

Simplifying
z = -16
Solution
z = {4, -16}