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Simplifying (5z + -7)(3 + z) = 0 Reorder the terms: (-7 + 5z)(3 + z) = 0 Multiply (-7 + 5z) * (3 + z) (-7(3 + z) + 5z * (3 + z)) = 0 ((3 * -7 + z * -7) + 5z * (3 + z)) = 0 ((-21 + -7z) + 5z * (3 + z)) = 0 (-21 + -7z + (3 * 5z + z * 5z)) = 0 (-21 + -7z + (15z + 5z2)) = 0 Combine like terms: -7z + 15z = 8z (-21 + 8z + 5z2) = 0 Solving -21 + 8z + 5z2 = 0 Solving for variable 'z'. Factor a trinomial. (-3 + -1z)(7 + -5z) = 0Subproblem 1
Set the factor '(-3 + -1z)' equal to zero and attempt to solve: Simplifying -3 + -1z = 0 Solving -3 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1z = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1z = 0 + 3 -1z = 0 + 3 Combine like terms: 0 + 3 = 3 -1z = 3 Divide each side by '-1'. z = -3 Simplifying z = -3Subproblem 2
Set the factor '(7 + -5z)' equal to zero and attempt to solve: Simplifying 7 + -5z = 0 Solving 7 + -5z = 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 + -5z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -5z = 0 + -7 -5z = 0 + -7 Combine like terms: 0 + -7 = -7 -5z = -7 Divide each side by '-5'. z = 1.4 Simplifying z = 1.4Solution
z = {-3, 1.4}
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