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Simplifying (4z + -5)(3z + -2) + -1(3z + -9)(3z + -2) = 0 Reorder the terms: (-5 + 4z)(3z + -2) + -1(3z + -9)(3z + -2) = 0 Reorder the terms: (-5 + 4z)(-2 + 3z) + -1(3z + -9)(3z + -2) = 0 Multiply (-5 + 4z) * (-2 + 3z) (-5(-2 + 3z) + 4z * (-2 + 3z)) + -1(3z + -9)(3z + -2) = 0 ((-2 * -5 + 3z * -5) + 4z * (-2 + 3z)) + -1(3z + -9)(3z + -2) = 0 ((10 + -15z) + 4z * (-2 + 3z)) + -1(3z + -9)(3z + -2) = 0 (10 + -15z + (-2 * 4z + 3z * 4z)) + -1(3z + -9)(3z + -2) = 0 (10 + -15z + (-8z + 12z2)) + -1(3z + -9)(3z + -2) = 0 Combine like terms: -15z + -8z = -23z (10 + -23z + 12z2) + -1(3z + -9)(3z + -2) = 0 Reorder the terms: 10 + -23z + 12z2 + -1(-9 + 3z)(3z + -2) = 0 Reorder the terms: 10 + -23z + 12z2 + -1(-9 + 3z)(-2 + 3z) = 0 Multiply (-9 + 3z) * (-2 + 3z) 10 + -23z + 12z2 + -1(-9(-2 + 3z) + 3z * (-2 + 3z)) = 0 10 + -23z + 12z2 + -1((-2 * -9 + 3z * -9) + 3z * (-2 + 3z)) = 0 10 + -23z + 12z2 + -1((18 + -27z) + 3z * (-2 + 3z)) = 0 10 + -23z + 12z2 + -1(18 + -27z + (-2 * 3z + 3z * 3z)) = 0 10 + -23z + 12z2 + -1(18 + -27z + (-6z + 9z2)) = 0 Combine like terms: -27z + -6z = -33z 10 + -23z + 12z2 + -1(18 + -33z + 9z2) = 0 10 + -23z + 12z2 + (18 * -1 + -33z * -1 + 9z2 * -1) = 0 10 + -23z + 12z2 + (-18 + 33z + -9z2) = 0 Reorder the terms: 10 + -18 + -23z + 33z + 12z2 + -9z2 = 0 Combine like terms: 10 + -18 = -8 -8 + -23z + 33z + 12z2 + -9z2 = 0 Combine like terms: -23z + 33z = 10z -8 + 10z + 12z2 + -9z2 = 0 Combine like terms: 12z2 + -9z2 = 3z2 -8 + 10z + 3z2 = 0 Solving -8 + 10z + 3z2 = 0 Solving for variable 'z'. Factor a trinomial. (-4 + -1z)(2 + -3z) = 0Subproblem 1
Set the factor '(-4 + -1z)' equal to zero and attempt to solve: Simplifying -4 + -1z = 0 Solving -4 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1z = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1z = 0 + 4 -1z = 0 + 4 Combine like terms: 0 + 4 = 4 -1z = 4 Divide each side by '-1'. z = -4 Simplifying z = -4Subproblem 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 = {-4, 0.6666666667}
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