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Simplifying 0 = 3z2 + -13z + -10 Reorder the terms: 0 = -10 + -13z + 3z2 Solving 0 = -10 + -13z + 3z2 Solving for variable 'z'. Combine like terms: 0 + 10 = 10 10 + 13z + -3z2 = -10 + -13z + 3z2 + 10 + 13z + -3z2 Reorder the terms: 10 + 13z + -3z2 = -10 + 10 + -13z + 13z + 3z2 + -3z2 Combine like terms: -10 + 10 = 0 10 + 13z + -3z2 = 0 + -13z + 13z + 3z2 + -3z2 10 + 13z + -3z2 = -13z + 13z + 3z2 + -3z2 Combine like terms: -13z + 13z = 0 10 + 13z + -3z2 = 0 + 3z2 + -3z2 10 + 13z + -3z2 = 3z2 + -3z2 Combine like terms: 3z2 + -3z2 = 0 10 + 13z + -3z2 = 0 Factor a trinomial. (5 + -1z)(2 + 3z) = 0Subproblem 1
Set the factor '(5 + -1z)' equal to zero and attempt to solve: Simplifying 5 + -1z = 0 Solving 5 + -1z = 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 + -1z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1z = 0 + -5 -1z = 0 + -5 Combine like terms: 0 + -5 = -5 -1z = -5 Divide each side by '-1'. z = 5 Simplifying z = 5Subproblem 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 = {5, -0.6666666667}
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