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Simplifying (2 + -1z)(4z + 7) = 0 Reorder the terms: (2 + -1z)(7 + 4z) = 0 Multiply (2 + -1z) * (7 + 4z) (2(7 + 4z) + -1z * (7 + 4z)) = 0 ((7 * 2 + 4z * 2) + -1z * (7 + 4z)) = 0 ((14 + 8z) + -1z * (7 + 4z)) = 0 (14 + 8z + (7 * -1z + 4z * -1z)) = 0 (14 + 8z + (-7z + -4z2)) = 0 Combine like terms: 8z + -7z = 1z (14 + 1z + -4z2) = 0 Solving 14 + 1z + -4z2 = 0 Solving for variable 'z'. Factor a trinomial. (2 + -1z)(7 + 4z) = 0Subproblem 1
Set the factor '(2 + -1z)' equal to zero and attempt to solve: Simplifying 2 + -1z = 0 Solving 2 + -1z = 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 + -1z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1z = 0 + -2 -1z = 0 + -2 Combine like terms: 0 + -2 = -2 -1z = -2 Divide each side by '-1'. z = 2 Simplifying z = 2Subproblem 2
Set the factor '(7 + 4z)' equal to zero and attempt to solve: Simplifying 7 + 4z = 0 Solving 7 + 4z = 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 + 4z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 4z = 0 + -7 4z = 0 + -7 Combine like terms: 0 + -7 = -7 4z = -7 Divide each side by '4'. z = -1.75 Simplifying z = -1.75Solution
z = {2, -1.75}
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