(5z-2)(6z-7)=0

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Solution for (5z-2)(6z-7)=0 equation: 


Simplifying
(5z + -2)(6z + -7) = 0

Reorder the terms:
(-2 + 5z)(6z + -7) = 0

Reorder the terms:
(-2 + 5z)(-7 + 6z) = 0

Multiply (-2 + 5z) * (-7 + 6z)
(-2(-7 + 6z) + 5z * (-7 + 6z)) = 0
((-7 * -2 + 6z * -2) + 5z * (-7 + 6z)) = 0
((14 + -12z) + 5z * (-7 + 6z)) = 0
(14 + -12z + (-7 * 5z + 6z * 5z)) = 0
(14 + -12z + (-35z + 30z2)) = 0

Combine like terms: -12z + -35z = -47z
(14 + -47z + 30z2) = 0

Solving
14 + -47z + 30z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(2 + -5z)(7 + -6z) = 0


Subproblem 1
Set the factor '(2 + -5z)' equal to zero and attempt to solve:

Simplifying
2 + -5z = 0

Solving
2 + -5z = 0

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

Add '-2' to each side of the equation.
2 + -2 + -5z = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5z = 0 + -2
-5z = 0 + -2

Combine like terms: 0 + -2 = -2
-5z = -2

Divide each side by '-5'.
z = 0.4

Simplifying
z = 0.4

Subproblem 2
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
Solution
z = {0.4, 1.166666667}

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