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

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


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

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

Multiply (-9 + 2z) * (2 + z)
(-9(2 + z) + 2z * (2 + z)) = 0
((2 * -9 + z * -9) + 2z * (2 + z)) = 0
((-18 + -9z) + 2z * (2 + z)) = 0
(-18 + -9z + (2 * 2z + z * 2z)) = 0
(-18 + -9z + (4z + 2z2)) = 0

Combine like terms: -9z + 4z = -5z
(-18 + -5z + 2z2) = 0

Solving
-18 + -5z + 2z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-2 + -1z)(9 + -2z) = 0

Subproblem 1

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

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 = {-2, 4.5}

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