(6z-7)(11z+6)=0

Solution for (6z-7)(11z+6)=0 equation:

Simplifying
(6z + -7)(11z + 6) = 0

Reorder the terms:
(-7 + 6z)(11z + 6) = 0

Reorder the terms:
(-7 + 6z)(6 + 11z) = 0

Multiply (-7 + 6z) * (6 + 11z)
(-7(6 + 11z) + 6z * (6 + 11z)) = 0
((6 * -7 + 11z * -7) + 6z * (6 + 11z)) = 0
((-42 + -77z) + 6z * (6 + 11z)) = 0
(-42 + -77z + (6 * 6z + 11z * 6z)) = 0
(-42 + -77z + (36z + 66z2)) = 0

Combine like terms: -77z + 36z = -41z
(-42 + -41z + 66z2) = 0

Solving
-42 + -41z + 66z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-6 + -11z)(7 + -6z) = 0

Subproblem 1
Set the factor '(-6 + -11z)' equal to zero and attempt to solve:

Simplifying
-6 + -11z = 0

Solving
-6 + -11z = 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 + -11z = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -11z = 0 + 6
-11z = 0 + 6

Combine like terms: 0 + 6 = 6
-11z = 6

Divide each side by '-11'.
z = -0.5454545455

Simplifying
z = -0.5454545455
Subproblem 2
Set the factor '(7 + -6z)' equal to zero and attempt to solve:

Simplifying
7 + -6z = 0

Solving
7 + -6z = 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 + -6z = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -6z = 0 + -7
-6z = 0 + -7

Combine like terms: 0 + -7 = -7
-6z = -7

Divide each side by '-6'.
z = 1.166666667

Simplifying
z = 1.166666667
Solution
z = {-0.5454545455, 1.166666667}