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

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


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

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

Multiply (8 + 3z) * (3 + -1z)
(8(3 + -1z) + 3z * (3 + -1z)) = 0
((3 * 8 + -1z * 8) + 3z * (3 + -1z)) = 0
((24 + -8z) + 3z * (3 + -1z)) = 0
(24 + -8z + (3 * 3z + -1z * 3z)) = 0
(24 + -8z + (9z + -3z2)) = 0

Combine like terms: -8z + 9z = 1z
(24 + 1z + -3z2) = 0

Solving
24 + 1z + -3z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(3 + -1z)(8 + 3z) = 0

Subproblem 1

Set the factor '(3 + -1z)' equal to zero and attempt to solve: Simplifying 3 + -1z = 0 Solving 3 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1z = 0 + -3 -1z = 0 + -3 Combine like terms: 0 + -3 = -3 -1z = -3 Divide each side by '-1'. z = 3 Simplifying z = 3

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 = {3, -2.666666667}

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