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

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


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

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

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

Multiply (7 + z) * (-5 + -1z)
5(7(-5 + -1z) + z(-5 + -1z)) = 0
5((-5 * 7 + -1z * 7) + z(-5 + -1z)) = 0
5((-35 + -7z) + z(-5 + -1z)) = 0
5(-35 + -7z + (-5 * z + -1z * z)) = 0
5(-35 + -7z + (-5z + -1z2)) = 0

Combine like terms: -7z + -5z = -12z
5(-35 + -12z + -1z2) = 0
(-35 * 5 + -12z * 5 + -1z2 * 5) = 0
(-175 + -60z + -5z2) = 0

Solving
-175 + -60z + -5z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '-5'.
-5(35 + 12z + z2) = 0

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

Ignore the factor -5.

Subproblem 1
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

Subproblem 2
Set the factor '(5 + z)' equal to zero and attempt to solve:

Simplifying
5 + z = 0

Solving
5 + z = 0

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

Add '-5' to each side of the equation.
5 + -5 + z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + z = 0 + -5
z = 0 + -5

Combine like terms: 0 + -5 = -5
z = -5

Simplifying
z = -5
Solution
z = {-7, -5}

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