(8z-6)(12z+14)=0

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Solution for (8z-6)(12z+14)=0 equation: 


Simplifying
(8z + -6)(12z + 14) = 0

Reorder the terms:
(-6 + 8z)(12z + 14) = 0

Reorder the terms:
(-6 + 8z)(14 + 12z) = 0

Multiply (-6 + 8z) * (14 + 12z)
(-6(14 + 12z) + 8z * (14 + 12z)) = 0
((14 * -6 + 12z * -6) + 8z * (14 + 12z)) = 0
((-84 + -72z) + 8z * (14 + 12z)) = 0
(-84 + -72z + (14 * 8z + 12z * 8z)) = 0
(-84 + -72z + (112z + 96z2)) = 0

Combine like terms: -72z + 112z = 40z
(-84 + 40z + 96z2) = 0

Solving
-84 + 40z + 96z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-21 + 10z + 24z2) = 0

Factor a trinomial.
4((-7 + -6z)(3 + -4z)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-7 + -6z)' equal to zero and attempt to solve:

Simplifying
-7 + -6z = 0

Solving
-7 + -6z = 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 + -6z = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -6z = 0 + 7
-6z = 0 + 7

Combine like terms: 0 + 7 = 7
-6z = 7

Divide each side by '-6'.
z = -1.166666667

Simplifying
z = -1.166666667

Subproblem 2
Set the factor '(3 + -4z)' equal to zero and attempt to solve:

Simplifying
3 + -4z = 0

Solving
3 + -4z = 0

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

Add '-3' to each side of the equation.
3 + -3 + -4z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4z = 0 + -3
-4z = 0 + -3

Combine like terms: 0 + -3 = -3
-4z = -3

Divide each side by '-4'.
z = 0.75

Simplifying
z = 0.75
Solution
z = {-1.166666667, 0.75}

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