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Simplifying 6z2 + 5z = 14 Reorder the terms: 5z + 6z2 = 14 Solving 5z + 6z2 = 14 Solving for variable 'z'. Reorder the terms: -14 + 5z + 6z2 = 14 + -14 Combine like terms: 14 + -14 = 0 -14 + 5z + 6z2 = 0 Factor a trinomial. (-2 + -1z)(7 + -6z) = 0Subproblem 1
Set the factor '(-2 + -1z)' equal to zero and attempt to solve: Simplifying -2 + -1z = 0 Solving -2 + -1z = 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 + -1z = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1z = 0 + 2 -1z = 0 + 2 Combine like terms: 0 + 2 = 2 -1z = 2 Divide each side by '-1'. z = -2 Simplifying z = -2Subproblem 2
Set the factor '(7 + -6z)' equal to zero and attempt to solve: Simplifying 7 + -6z = 0 Solving 7 + -6z = 0 Move all terms containing z to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -6z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -6z = 0 + -7 -6z = 0 + -7 Combine like terms: 0 + -7 = -7 -6z = -7 Divide each side by '-6'. z = 1.166666667 Simplifying z = 1.166666667Solution
z = {-2, 1.166666667}
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