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

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Solution for 5(z-6)(-z-7)=0 equation: 


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

Reorder the terms:
5(-6 + z)(-1z + -7) = 0

Reorder the terms:
5(-6 + z)(-7 + -1z) = 0

Multiply (-6 + z) * (-7 + -1z)
5(-6(-7 + -1z) + z(-7 + -1z)) = 0
5((-7 * -6 + -1z * -6) + z(-7 + -1z)) = 0
5((42 + 6z) + z(-7 + -1z)) = 0
5(42 + 6z + (-7 * z + -1z * z)) = 0
5(42 + 6z + (-7z + -1z2)) = 0

Combine like terms: 6z + -7z = -1z
5(42 + -1z + -1z2) = 0
(42 * 5 + -1z * 5 + -1z2 * 5) = 0
(210 + -5z + -5z2) = 0

Solving
210 + -5z + -5z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '5'.
5(42 + -1z + -1z2) = 0

Factor a trinomial.
5((6 + -1z)(7 + z)) = 0

Ignore the factor 5.

Subproblem 1
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

Subproblem 2
Set the factor '(7 + z)' equal to zero and attempt to solve:

Simplifying
7 + z = 0

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

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

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

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

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