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Simplifying (4z + -5)(3z + -2) = 0 Reorder the terms: (-5 + 4z)(3z + -2) = 0 Reorder the terms: (-5 + 4z)(-2 + 3z) = 0 Multiply (-5 + 4z) * (-2 + 3z) (-5(-2 + 3z) + 4z * (-2 + 3z)) = 0 ((-2 * -5 + 3z * -5) + 4z * (-2 + 3z)) = 0 ((10 + -15z) + 4z * (-2 + 3z)) = 0 (10 + -15z + (-2 * 4z + 3z * 4z)) = 0 (10 + -15z + (-8z + 12z2)) = 0 Combine like terms: -15z + -8z = -23z (10 + -23z + 12z2) = 0 Solving 10 + -23z + 12z2 = 0 Solving for variable 'z'. Factor a trinomial. (2 + -3z)(5 + -4z) = 0Subproblem 1
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 = 0.6666666667Subproblem 2
Set the factor '(5 + -4z)' equal to zero and attempt to solve: Simplifying 5 + -4z = 0 Solving 5 + -4z = 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 + -4z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4z = 0 + -5 -4z = 0 + -5 Combine like terms: 0 + -5 = -5 -4z = -5 Divide each side by '-4'. z = 1.25 Simplifying z = 1.25Solution
z = {0.6666666667, 1.25}
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