(6+z)(3z-8)=0

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Solution for (6+z)(3z-8)=0 equation:


Simplifying
(6 + z)(3z + -8) = 0

Reorder the terms:
(6 + z)(-8 + 3z) = 0

Multiply (6 + z) * (-8 + 3z)
(6(-8 + 3z) + z(-8 + 3z)) = 0
((-8 * 6 + 3z * 6) + z(-8 + 3z)) = 0
((-48 + 18z) + z(-8 + 3z)) = 0
(-48 + 18z + (-8 * z + 3z * z)) = 0
(-48 + 18z + (-8z + 3z2)) = 0

Combine like terms: 18z + -8z = 10z
(-48 + 10z + 3z2) = 0

Solving
-48 + 10z + 3z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-6 + -1z)(8 + -3z) = 0

Subproblem 1

Set the factor '(-6 + -1z)' equal to zero and attempt to solve: Simplifying -6 + -1z = 0 Solving -6 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1z = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1z = 0 + 6 -1z = 0 + 6 Combine like terms: 0 + 6 = 6 -1z = 6 Divide each side by '-1'. z = -6 Simplifying z = -6

Subproblem 2

Set the factor '(8 + -3z)' equal to zero and attempt to solve: Simplifying 8 + -3z = 0 Solving 8 + -3z = 0 Move all terms containing z to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -3z = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3z = 0 + -8 -3z = 0 + -8 Combine like terms: 0 + -8 = -8 -3z = -8 Divide each side by '-3'. z = 2.666666667 Simplifying z = 2.666666667

Solution

z = {-6, 2.666666667}

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