18+2z=z^2-5z

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Solution for 18+2z=z^2-5z equation:


Simplifying
18 + 2z = z2 + -5z

Reorder the terms:
18 + 2z = -5z + z2

Solving
18 + 2z = -5z + z2

Solving for variable 'z'.

Combine like terms: 2z + 5z = 7z
18 + 7z + -1z2 = -5z + z2 + 5z + -1z2

Reorder the terms:
18 + 7z + -1z2 = -5z + 5z + z2 + -1z2

Combine like terms: -5z + 5z = 0
18 + 7z + -1z2 = 0 + z2 + -1z2
18 + 7z + -1z2 = z2 + -1z2

Combine like terms: z2 + -1z2 = 0
18 + 7z + -1z2 = 0

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

Subproblem 1

Set the factor '(9 + -1z)' equal to zero and attempt to solve: Simplifying 9 + -1z = 0 Solving 9 + -1z = 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 + -1z = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1z = 0 + -9 -1z = 0 + -9 Combine like terms: 0 + -9 = -9 -1z = -9 Divide each side by '-1'. z = 9 Simplifying z = 9

Subproblem 2

Set the factor '(2 + z)' equal to zero and attempt to solve: Simplifying 2 + z = 0 Solving 2 + z = 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 + z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + z = 0 + -2 z = 0 + -2 Combine like terms: 0 + -2 = -2 z = -2 Simplifying z = -2

Solution

z = {9, -2}

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