z*z+3(z-2)=48

Solution for z*z+3(z-2)=48 equation:

Simplifying
z * z + 3(z + -2) = 48

Multiply z * z
z2 + 3(z + -2) = 48

Reorder the terms:
z2 + 3(-2 + z) = 48
z2 + (-2 * 3 + z * 3) = 48
z2 + (-6 + 3z) = 48

Reorder the terms:
-6 + 3z + z2 = 48

Solving
-6 + 3z + z2 = 48

Solving for variable 'z'.

Reorder the terms:
-6 + -48 + 3z + z2 = 48 + -48

Combine like terms: -6 + -48 = -54
-54 + 3z + z2 = 48 + -48

Combine like terms: 48 + -48 = 0
-54 + 3z + z2 = 0

Factor a trinomial.
(-9 + -1z)(6 + -1z) = 0

Subproblem 1
Set the factor '(-9 + -1z)' equal to zero and attempt to solve:

Simplifying
-9 + -1z = 0

Solving
-9 + -1z = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1z = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1z = 0 + 9
-1z = 0 + 9

Combine like terms: 0 + 9 = 9
-1z = 9

Divide each side by '-1'.
z = -9

Simplifying
z = -9
Subproblem 2
Set the factor '(6 + -1z)' equal to zero and attempt to solve:

Simplifying
6 + -1z = 0

Solving
6 + -1z = 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 + -1z = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1z = 0 + -6
-1z = 0 + -6

Combine like terms: 0 + -6 = -6
-1z = -6

Divide each side by '-1'.
z = 6

Simplifying
z = 6
Solution
z = {-9, 6}