(8+z)(2z-9)=0

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Solution for (8+z)(2z-9)=0 equation:


Simplifying
(8 + z)(2z + -9) = 0

Reorder the terms:
(8 + z)(-9 + 2z) = 0

Multiply (8 + z) * (-9 + 2z)
(8(-9 + 2z) + z(-9 + 2z)) = 0
((-9 * 8 + 2z * 8) + z(-9 + 2z)) = 0
((-72 + 16z) + z(-9 + 2z)) = 0
(-72 + 16z + (-9 * z + 2z * z)) = 0
(-72 + 16z + (-9z + 2z2)) = 0

Combine like terms: 16z + -9z = 7z
(-72 + 7z + 2z2) = 0

Solving
-72 + 7z + 2z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-8 + -1z)(9 + -2z) = 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 '(9 + -2z)' equal to zero and attempt to solve: Simplifying 9 + -2z = 0 Solving 9 + -2z = 0 Move all terms containing z to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -2z = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2z = 0 + -9 -2z = 0 + -9 Combine like terms: 0 + -9 = -9 -2z = -9 Divide each side by '-2'. z = 4.5 Simplifying z = 4.5

Solution

z = {-8, 4.5}

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