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Simplifying (7 + z)(5z + -8) = 0 Reorder the terms: (7 + z)(-8 + 5z) = 0 Multiply (7 + z) * (-8 + 5z) (7(-8 + 5z) + z(-8 + 5z)) = 0 ((-8 * 7 + 5z * 7) + z(-8 + 5z)) = 0 ((-56 + 35z) + z(-8 + 5z)) = 0 (-56 + 35z + (-8 * z + 5z * z)) = 0 (-56 + 35z + (-8z + 5z2)) = 0 Combine like terms: 35z + -8z = 27z (-56 + 27z + 5z2) = 0 Solving -56 + 27z + 5z2 = 0 Solving for variable 'z'. Factor a trinomial. (-7 + -1z)(8 + -5z) = 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 '(8 + -5z)' equal to zero and attempt to solve: Simplifying 8 + -5z = 0 Solving 8 + -5z = 0 Move all terms containing z to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -5z = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -5z = 0 + -8 -5z = 0 + -8 Combine like terms: 0 + -8 = -8 -5z = -8 Divide each side by '-5'. z = 1.6 Simplifying z = 1.6Solution
z = {-7, 1.6}
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