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Simplifying (4z + 3)(7 + -1z) = 0 Reorder the terms: (3 + 4z)(7 + -1z) = 0 Multiply (3 + 4z) * (7 + -1z) (3(7 + -1z) + 4z * (7 + -1z)) = 0 ((7 * 3 + -1z * 3) + 4z * (7 + -1z)) = 0 ((21 + -3z) + 4z * (7 + -1z)) = 0 (21 + -3z + (7 * 4z + -1z * 4z)) = 0 (21 + -3z + (28z + -4z2)) = 0 Combine like terms: -3z + 28z = 25z (21 + 25z + -4z2) = 0 Solving 21 + 25z + -4z2 = 0 Solving for variable 'z'. Factor a trinomial. (7 + -1z)(3 + 4z) = 0Subproblem 1
Set the factor '(7 + -1z)' equal to zero and attempt to solve: Simplifying 7 + -1z = 0 Solving 7 + -1z = 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 + -1z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1z = 0 + -7 -1z = 0 + -7 Combine like terms: 0 + -7 = -7 -1z = -7 Divide each side by '-1'. z = 7 Simplifying z = 7Subproblem 2
Set the factor '(3 + 4z)' equal to zero and attempt to solve: Simplifying 3 + 4z = 0 Solving 3 + 4z = 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 + 4z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4z = 0 + -3 4z = 0 + -3 Combine like terms: 0 + -3 = -3 4z = -3 Divide each side by '4'. z = -0.75 Simplifying z = -0.75Solution
z = {7, -0.75}
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