18z^2-48z-130=0

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Solution for 18z^2-48z-130=0 equation:


Simplifying
18z2 + -48z + -130 = 0

Reorder the terms:
-130 + -48z + 18z2 = 0

Solving
-130 + -48z + 18z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-65 + -24z + 9z2) = 0

Factor a trinomial.
2((-5 + -3z)(13 + -3z)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-5 + -3z)' equal to zero and attempt to solve: Simplifying -5 + -3z = 0 Solving -5 + -3z = 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 + -3z = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -3z = 0 + 5 -3z = 0 + 5 Combine like terms: 0 + 5 = 5 -3z = 5 Divide each side by '-3'. z = -1.666666667 Simplifying z = -1.666666667

Subproblem 2

Set the factor '(13 + -3z)' equal to zero and attempt to solve: Simplifying 13 + -3z = 0 Solving 13 + -3z = 0 Move all terms containing z to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -3z = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -3z = 0 + -13 -3z = 0 + -13 Combine like terms: 0 + -13 = -13 -3z = -13 Divide each side by '-3'. z = 4.333333333 Simplifying z = 4.333333333

Solution

z = {-1.666666667, 4.333333333}

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