2z^2-42z+76=

Solution for 2z^2-42z+76= equation:

Simplifying
2z2 + -42z + 76 = 0

Reorder the terms:
76 + -42z + 2z2 = 0

Solving
76 + -42z + 2z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '2'.
2(38 + -21z + z2) = 0

Factor a trinomial.
2((2 + -1z)(19 + -1z)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(2 + -1z)' equal to zero and attempt to solve:

Simplifying
2 + -1z = 0

Solving
2 + -1z = 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 + -1z = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1z = 0 + -2
-1z = 0 + -2

Combine like terms: 0 + -2 = -2
-1z = -2

Divide each side by '-1'.
z = 2

Simplifying
z = 2
Subproblem 2
Set the factor '(19 + -1z)' equal to zero and attempt to solve:

Simplifying
19 + -1z = 0

Solving
19 + -1z = 0

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

Add '-19' to each side of the equation.
19 + -19 + -1z = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -1z = 0 + -19
-1z = 0 + -19

Combine like terms: 0 + -19 = -19
-1z = -19

Divide each side by '-1'.
z = 19

Simplifying
z = 19
Solution
z = {2, 19}