(7+z)(3z+8)=0

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Solution for (7+z)(3z+8)=0 equation: 


Simplifying
(7 + z)(3z + 8) = 0

Reorder the terms:
(7 + z)(8 + 3z) = 0

Multiply (7 + z) * (8 + 3z)
(7(8 + 3z) + z(8 + 3z)) = 0
((8 * 7 + 3z * 7) + z(8 + 3z)) = 0
((56 + 21z) + z(8 + 3z)) = 0
(56 + 21z + (8 * z + 3z * z)) = 0
(56 + 21z + (8z + 3z2)) = 0

Combine like terms: 21z + 8z = 29z
(56 + 29z + 3z2) = 0

Solving
56 + 29z + 3z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(7 + z)(8 + 3z) = 0


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

Simplifying
7 + z = 0

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

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

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

Simplifying
z = -7

Subproblem 2
Set the factor '(8 + 3z)' equal to zero and attempt to solve:

Simplifying
8 + 3z = 0

Solving
8 + 3z = 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 + 3z = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 3z = 0 + -8
3z = 0 + -8

Combine like terms: 0 + -8 = -8
3z = -8

Divide each side by '3'.
z = -2.666666667

Simplifying
z = -2.666666667
Solution
z = {-7, -2.666666667}

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