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Simplifying 12z2 + z = 6 Reorder the terms: z + 12z2 = 6 Solving z + 12z2 = 6 Solving for variable 'z'. Reorder the terms: -6 + z + 12z2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + z + 12z2 = 0 Factor a trinomial. (-3 + -4z)(2 + -3z) = 0Subproblem 1
Set the factor '(-3 + -4z)' equal to zero and attempt to solve: Simplifying -3 + -4z = 0 Solving -3 + -4z = 0 Move all terms containing z to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -4z = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4z = 0 + 3 -4z = 0 + 3 Combine like terms: 0 + 3 = 3 -4z = 3 Divide each side by '-4'. z = -0.75 Simplifying z = -0.75Subproblem 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 = 0.6666666667Solution
z = {-0.75, 0.6666666667}
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