4z^2-7z-57=0

Solution for 4z^2-7z-57=0 equation:

Simplifying
4z2 + -7z + -57 = 0

Reorder the terms:
-57 + -7z + 4z2 = 0

Solving
-57 + -7z + 4z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-3 + -1z)(19 + -4z) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(19 + -4z)' equal to zero and attempt to solve:

Simplifying
19 + -4z = 0

Solving
19 + -4z = 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 + -4z = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -4z = 0 + -19
-4z = 0 + -19

Combine like terms: 0 + -19 = -19
-4z = -19

Divide each side by '-4'.
z = 4.75

Simplifying
z = 4.75
Solution
z = {-3, 4.75}