z(2z-3)=14

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Solution for z(2z-3)=14 equation:


Simplifying
z(2z + -3) = 14

Reorder the terms:
z(-3 + 2z) = 14
(-3 * z + 2z * z) = 14
(-3z + 2z2) = 14

Solving
-3z + 2z2 = 14

Solving for variable 'z'.

Reorder the terms:
-14 + -3z + 2z2 = 14 + -14

Combine like terms: 14 + -14 = 0
-14 + -3z + 2z2 = 0

Factor a trinomial.
(-2 + -1z)(7 + -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 '(7 + -2z)' equal to zero and attempt to solve: Simplifying 7 + -2z = 0 Solving 7 + -2z = 0 Move all terms containing z to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -2z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2z = 0 + -7 -2z = 0 + -7 Combine like terms: 0 + -7 = -7 -2z = -7 Divide each side by '-2'. z = 3.5 Simplifying z = 3.5

Solution

z = {-2, 3.5}

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