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

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


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

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

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