-4(z-6)(-z-7)=0

Solution for -4(z-6)(-z-7)=0 equation:

Simplifying
-4(z + -6)(-1z + -7) = 0

Reorder the terms:
-4(-6 + z)(-1z + -7) = 0

Reorder the terms:
-4(-6 + z)(-7 + -1z) = 0

Multiply (-6 + z) * (-7 + -1z)
-4(-6(-7 + -1z) + z(-7 + -1z)) = 0
-4((-7 * -6 + -1z * -6) + z(-7 + -1z)) = 0
-4((42 + 6z) + z(-7 + -1z)) = 0
-4(42 + 6z + (-7 * z + -1z * z)) = 0
-4(42 + 6z + (-7z + -1z2)) = 0

Combine like terms: 6z + -7z = -1z
-4(42 + -1z + -1z2) = 0
(42 * -4 + -1z * -4 + -1z2 * -4) = 0
(-168 + 4z + 4z2) = 0

Solving
-168 + 4z + 4z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-42 + z + z2) = 0

Factor a trinomial.
4((-7 + -1z)(6 + -1z)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-7 + -1z)' equal to zero and attempt to solve:

Simplifying
-7 + -1z = 0

Solving
-7 + -1z = 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 + -1z = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1z = 0 + 7
-1z = 0 + 7

Combine like terms: 0 + 7 = 7
-1z = 7

Divide each side by '-1'.
z = -7

Simplifying
z = -7
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 = {-7, 6}