(8+z)(4z-5)=0

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Solution for (8+z)(4z-5)=0 equation:


Simplifying
(8 + z)(4z + -5) = 0

Reorder the terms:
(8 + z)(-5 + 4z) = 0

Multiply (8 + z) * (-5 + 4z)
(8(-5 + 4z) + z(-5 + 4z)) = 0
((-5 * 8 + 4z * 8) + z(-5 + 4z)) = 0
((-40 + 32z) + z(-5 + 4z)) = 0
(-40 + 32z + (-5 * z + 4z * z)) = 0
(-40 + 32z + (-5z + 4z2)) = 0

Combine like terms: 32z + -5z = 27z
(-40 + 27z + 4z2) = 0

Solving
-40 + 27z + 4z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-8 + -1z)(5 + -4z) = 0

Subproblem 1

Set the factor '(-8 + -1z)' equal to zero and attempt to solve: Simplifying -8 + -1z = 0 Solving -8 + -1z = 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 + -1z = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1z = 0 + 8 -1z = 0 + 8 Combine like terms: 0 + 8 = 8 -1z = 8 Divide each side by '-1'. z = -8 Simplifying z = -8

Subproblem 2

Set the factor '(5 + -4z)' equal to zero and attempt to solve: Simplifying 5 + -4z = 0 Solving 5 + -4z = 0 Move all terms containing z to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -4z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4z = 0 + -5 -4z = 0 + -5 Combine like terms: 0 + -5 = -5 -4z = -5 Divide each side by '-4'. z = 1.25 Simplifying z = 1.25

Solution

z = {-8, 1.25}

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