(8z-14)(7z-8)=0

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Solution for (8z-14)(7z-8)=0 equation: 


Simplifying
(8z + -14)(7z + -8) = 0

Reorder the terms:
(-14 + 8z)(7z + -8) = 0

Reorder the terms:
(-14 + 8z)(-8 + 7z) = 0

Multiply (-14 + 8z) * (-8 + 7z)
(-14(-8 + 7z) + 8z * (-8 + 7z)) = 0
((-8 * -14 + 7z * -14) + 8z * (-8 + 7z)) = 0
((112 + -98z) + 8z * (-8 + 7z)) = 0
(112 + -98z + (-8 * 8z + 7z * 8z)) = 0
(112 + -98z + (-64z + 56z2)) = 0

Combine like terms: -98z + -64z = -162z
(112 + -162z + 56z2) = 0

Solving
112 + -162z + 56z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '2'.
2(56 + -81z + 28z2) = 0

Factor a trinomial.
2((8 + -7z)(7 + -4z)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(8 + -7z)' equal to zero and attempt to solve:

Simplifying
8 + -7z = 0

Solving
8 + -7z = 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 + -7z = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -7z = 0 + -8
-7z = 0 + -8

Combine like terms: 0 + -8 = -8
-7z = -8

Divide each side by '-7'.
z = 1.142857143

Simplifying
z = 1.142857143

Subproblem 2
Set the factor '(7 + -4z)' equal to zero and attempt to solve:

Simplifying
7 + -4z = 0

Solving
7 + -4z = 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 + -4z = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -4z = 0 + -7
-4z = 0 + -7

Combine like terms: 0 + -7 = -7
-4z = -7

Divide each side by '-4'.
z = 1.75

Simplifying
z = 1.75
Solution
z = {1.142857143, 1.75}

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