5(z+8)(-z+7)=0

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Solution for 5(z+8)(-z+7)=0 equation: 


Simplifying
5(z + 8)(-1z + 7) = 0

Reorder the terms:
5(8 + z)(-1z + 7) = 0

Reorder the terms:
5(8 + z)(7 + -1z) = 0

Multiply (8 + z) * (7 + -1z)
5(8(7 + -1z) + z(7 + -1z)) = 0
5((7 * 8 + -1z * 8) + z(7 + -1z)) = 0
5((56 + -8z) + z(7 + -1z)) = 0
5(56 + -8z + (7 * z + -1z * z)) = 0
5(56 + -8z + (7z + -1z2)) = 0

Combine like terms: -8z + 7z = -1z
5(56 + -1z + -1z2) = 0
(56 * 5 + -1z * 5 + -1z2 * 5) = 0
(280 + -5z + -5z2) = 0

Solving
280 + -5z + -5z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '5'.
5(56 + -1z + -1z2) = 0

Factor a trinomial.
5((7 + -1z)(8 + z)) = 0

Ignore the factor 5.

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 '(8 + z)' equal to zero and attempt to solve:

Simplifying
8 + z = 0

Solving
8 + z = 0

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

Add '-8' to each side of the equation.
8 + -8 + z = 0 + -8

Combine like terms: 8 + -8 = 0
0 + z = 0 + -8
z = 0 + -8

Combine like terms: 0 + -8 = -8
z = -8

Simplifying
z = -8
Solution
z = {7, -8}

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