(3-z)(5z+8)=0

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Solution for (3-z)(5z+8)=0 equation:


Simplifying
(3 + -1z)(5z + 8) = 0

Reorder the terms:
(3 + -1z)(8 + 5z) = 0

Multiply (3 + -1z) * (8 + 5z)
(3(8 + 5z) + -1z * (8 + 5z)) = 0
((8 * 3 + 5z * 3) + -1z * (8 + 5z)) = 0
((24 + 15z) + -1z * (8 + 5z)) = 0
(24 + 15z + (8 * -1z + 5z * -1z)) = 0
(24 + 15z + (-8z + -5z2)) = 0

Combine like terms: 15z + -8z = 7z
(24 + 7z + -5z2) = 0

Solving
24 + 7z + -5z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(3 + -1z)(8 + 5z) = 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 + 5z)' equal to zero and attempt to solve: Simplifying 8 + 5z = 0 Solving 8 + 5z = 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 + 5z = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 5z = 0 + -8 5z = 0 + -8 Combine like terms: 0 + -8 = -8 5z = -8 Divide each side by '5'. z = -1.6 Simplifying z = -1.6

Solution

z = {3, -1.6}

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