3z-5=-2z^2

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Solution for 3z-5=-2z^2 equation:


Simplifying
3z + -5 = -2z2

Reorder the terms:
-5 + 3z = -2z2

Solving
-5 + 3z = -2z2

Solving for variable 'z'.

Combine like terms: -2z2 + 2z2 = 0
-5 + 3z + 2z2 = 0

Factor a trinomial.
(-5 + -2z)(1 + -1z) = 0

Subproblem 1

Set the factor '(-5 + -2z)' equal to zero and attempt to solve: Simplifying -5 + -2z = 0 Solving -5 + -2z = 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 + -2z = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2z = 0 + 5 -2z = 0 + 5 Combine like terms: 0 + 5 = 5 -2z = 5 Divide each side by '-2'. z = -2.5 Simplifying z = -2.5

Subproblem 2

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

Solution

z = {-2.5, 1}

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