(3z+2)(7-z)=0

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Solution for (3z+2)(7-z)=0 equation: 


Simplifying
(3z + 2)(7 + -1z) = 0

Reorder the terms:
(2 + 3z)(7 + -1z) = 0

Multiply (2 + 3z) * (7 + -1z)
(2(7 + -1z) + 3z * (7 + -1z)) = 0
((7 * 2 + -1z * 2) + 3z * (7 + -1z)) = 0
((14 + -2z) + 3z * (7 + -1z)) = 0
(14 + -2z + (7 * 3z + -1z * 3z)) = 0
(14 + -2z + (21z + -3z2)) = 0

Combine like terms: -2z + 21z = 19z
(14 + 19z + -3z2) = 0

Solving
14 + 19z + -3z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(7 + -1z)(2 + 3z) = 0


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 '(2 + 3z)' equal to zero and attempt to solve:

Simplifying
2 + 3z = 0

Solving
2 + 3z = 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 + 3z = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3z = 0 + -2
3z = 0 + -2

Combine like terms: 0 + -2 = -2
3z = -2

Divide each side by '3'.
z = -0.6666666667

Simplifying
z = -0.6666666667
Solution
z = {7, -0.6666666667}

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