7z^2-84z+77=0

Solution for 7z^2-84z+77=0 equation:

Simplifying
7z2 + -84z + 77 = 0

Reorder the terms:
77 + -84z + 7z2 = 0

Solving
77 + -84z + 7z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '7'.
7(11 + -12z + z2) = 0

Factor a trinomial.
7((1 + -1z)(11 + -1z)) = 0

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

Simplifying
1 + -1z = 0

Solving
1 + -1z = 0

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

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

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

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

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

Simplifying
z = 1
Subproblem 2
Set the factor '(11 + -1z)' equal to zero and attempt to solve:

Simplifying
11 + -1z = 0

Solving
11 + -1z = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1z = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1z = 0 + -11
-1z = 0 + -11

Combine like terms: 0 + -11 = -11
-1z = -11

Divide each side by '-1'.
z = 11

Simplifying
z = 11
Solution
z = {1, 11}