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Simplifying 6z2 = -19z + -10 Reorder the terms: 6z2 = -10 + -19z Solving 6z2 = -10 + -19z Solving for variable 'z'. Reorder the terms: 10 + 19z + 6z2 = -10 + -19z + 10 + 19z Reorder the terms: 10 + 19z + 6z2 = -10 + 10 + -19z + 19z Combine like terms: -10 + 10 = 0 10 + 19z + 6z2 = 0 + -19z + 19z 10 + 19z + 6z2 = -19z + 19z Combine like terms: -19z + 19z = 0 10 + 19z + 6z2 = 0 Factor a trinomial. (5 + 2z)(2 + 3z) = 0Subproblem 1
Set the factor '(5 + 2z)' equal to zero and attempt to solve: Simplifying 5 + 2z = 0 Solving 5 + 2z = 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 + 2z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2z = 0 + -5 2z = 0 + -5 Combine like terms: 0 + -5 = -5 2z = -5 Divide each side by '2'. z = -2.5 Simplifying z = -2.5Subproblem 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 = {-2.5, -0.6666666667}
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