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Simplifying (4 + -1z)(5z + 3) = 0 Reorder the terms: (4 + -1z)(3 + 5z) = 0 Multiply (4 + -1z) * (3 + 5z) (4(3 + 5z) + -1z * (3 + 5z)) = 0 ((3 * 4 + 5z * 4) + -1z * (3 + 5z)) = 0 ((12 + 20z) + -1z * (3 + 5z)) = 0 (12 + 20z + (3 * -1z + 5z * -1z)) = 0 (12 + 20z + (-3z + -5z2)) = 0 Combine like terms: 20z + -3z = 17z (12 + 17z + -5z2) = 0 Solving 12 + 17z + -5z2 = 0 Solving for variable 'z'. Factor a trinomial. (4 + -1z)(3 + 5z) = 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 '(3 + 5z)' equal to zero and attempt to solve: Simplifying 3 + 5z = 0 Solving 3 + 5z = 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 + 5z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 5z = 0 + -3 5z = 0 + -3 Combine like terms: 0 + -3 = -3 5z = -3 Divide each side by '5'. z = -0.6 Simplifying z = -0.6Solution
z = {4, -0.6}
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