2z(z+2)=z^2+21

Solution for 2z(z+2)=z^2+21 equation:

Simplifying
2z(z + 2) = z2 + 21

Reorder the terms:
2z(2 + z) = z2 + 21
(2 * 2z + z * 2z) = z2 + 21
(4z + 2z2) = z2 + 21

Reorder the terms:
4z + 2z2 = 21 + z2

Solving
4z + 2z2 = 21 + z2

Solving for variable 'z'.

Reorder the terms:
-21 + 4z + 2z2 + -1z2 = 21 + z2 + -21 + -1z2

Combine like terms: 2z2 + -1z2 = 1z2
-21 + 4z + 1z2 = 21 + z2 + -21 + -1z2

Reorder the terms:
-21 + 4z + 1z2 = 21 + -21 + z2 + -1z2

Combine like terms: 21 + -21 = 0
-21 + 4z + 1z2 = 0 + z2 + -1z2
-21 + 4z + 1z2 = z2 + -1z2

Combine like terms: z2 + -1z2 = 0
-21 + 4z + 1z2 = 0

Factor a trinomial.
(-7 + -1z)(3 + -1z) = 0

Subproblem 1
Set the factor '(-7 + -1z)' equal to zero and attempt to solve:

Simplifying
-7 + -1z = 0

Solving
-7 + -1z = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1z = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1z = 0 + 7
-1z = 0 + 7

Combine like terms: 0 + 7 = 7
-1z = 7

Divide each side by '-1'.
z = -7

Simplifying
z = -7
Subproblem 2
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
Solution
z = {-7, 3}