3z^2+10z=8

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Solution for 3z^2+10z=8 equation:


Simplifying
3z2 + 10z = 8

Reorder the terms:
10z + 3z2 = 8

Solving
10z + 3z2 = 8

Solving for variable 'z'.

Reorder the terms:
-8 + 10z + 3z2 = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + 10z + 3z2 = 0

Factor a trinomial.
(-4 + -1z)(2 + -3z) = 0

Subproblem 1

Set the factor '(-4 + -1z)' equal to zero and attempt to solve: Simplifying -4 + -1z = 0 Solving -4 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1z = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1z = 0 + 4 -1z = 0 + 4 Combine like terms: 0 + 4 = 4 -1z = 4 Divide each side by '-1'. z = -4 Simplifying z = -4

Subproblem 2

Set the factor '(2 + -3z)' equal to zero and attempt to solve: Simplifying 2 + -3z = 0 Solving 2 + -3z = 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 + -3z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3z = 0 + -2 -3z = 0 + -2 Combine like terms: 0 + -2 = -2 -3z = -2 Divide each side by '-3'. z = 0.6666666667 Simplifying z = 0.6666666667

Solution

z = {-4, 0.6666666667}

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