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Simplifying (z + 3)(7z + -9) = 0 Reorder the terms: (3 + z)(7z + -9) = 0 Reorder the terms: (3 + z)(-9 + 7z) = 0 Multiply (3 + z) * (-9 + 7z) (3(-9 + 7z) + z(-9 + 7z)) = 0 ((-9 * 3 + 7z * 3) + z(-9 + 7z)) = 0 ((-27 + 21z) + z(-9 + 7z)) = 0 (-27 + 21z + (-9 * z + 7z * z)) = 0 (-27 + 21z + (-9z + 7z2)) = 0 Combine like terms: 21z + -9z = 12z (-27 + 12z + 7z2) = 0 Solving -27 + 12z + 7z2 = 0 Solving for variable 'z'. Factor a trinomial. (-3 + -1z)(9 + -7z) = 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 '(9 + -7z)' equal to zero and attempt to solve: Simplifying 9 + -7z = 0 Solving 9 + -7z = 0 Move all terms containing z to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -7z = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -7z = 0 + -9 -7z = 0 + -9 Combine like terms: 0 + -9 = -9 -7z = -9 Divide each side by '-7'. z = 1.285714286 Simplifying z = 1.285714286Solution
z = {-3, 1.285714286}
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