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

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


Simplifying
(3z + 8)(7 + -1z) = 0

Reorder the terms:
(8 + 3z)(7 + -1z) = 0

Multiply (8 + 3z) * (7 + -1z)
(8(7 + -1z) + 3z * (7 + -1z)) = 0
((7 * 8 + -1z * 8) + 3z * (7 + -1z)) = 0
((56 + -8z) + 3z * (7 + -1z)) = 0
(56 + -8z + (7 * 3z + -1z * 3z)) = 0
(56 + -8z + (21z + -3z2)) = 0

Combine like terms: -8z + 21z = 13z
(56 + 13z + -3z2) = 0

Solving
56 + 13z + -3z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(7 + -1z)(8 + 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 '(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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