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Simplifying (2z + -5)(6z + 7) = 0 Reorder the terms: (-5 + 2z)(6z + 7) = 0 Reorder the terms: (-5 + 2z)(7 + 6z) = 0 Multiply (-5 + 2z) * (7 + 6z) (-5(7 + 6z) + 2z * (7 + 6z)) = 0 ((7 * -5 + 6z * -5) + 2z * (7 + 6z)) = 0 ((-35 + -30z) + 2z * (7 + 6z)) = 0 (-35 + -30z + (7 * 2z + 6z * 2z)) = 0 (-35 + -30z + (14z + 12z2)) = 0 Combine like terms: -30z + 14z = -16z (-35 + -16z + 12z2) = 0 Solving -35 + -16z + 12z2 = 0 Solving for variable 'z'. Factor a trinomial. (-7 + -6z)(5 + -2z) = 0Subproblem 1
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 = -1.166666667Subproblem 2
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 = 2.5Solution
z = {-1.166666667, 2.5}
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