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Simplifying (7 + z)(2z + -5) = 0 Reorder the terms: (7 + z)(-5 + 2z) = 0 Multiply (7 + z) * (-5 + 2z) (7(-5 + 2z) + z(-5 + 2z)) = 0 ((-5 * 7 + 2z * 7) + z(-5 + 2z)) = 0 ((-35 + 14z) + z(-5 + 2z)) = 0 (-35 + 14z + (-5 * z + 2z * z)) = 0 (-35 + 14z + (-5z + 2z2)) = 0 Combine like terms: 14z + -5z = 9z (-35 + 9z + 2z2) = 0 Solving -35 + 9z + 2z2 = 0 Solving for variable 'z'. Factor a trinomial. (-7 + -1z)(5 + -2z) = 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 '(5 + -2z)' equal to zero and attempt to solve: Simplifying 5 + -2z = 0 Solving 5 + -2z = 0 Move all terms containing z to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2z = 0 + -5 -2z = 0 + -5 Combine like terms: 0 + -5 = -5 -2z = -5 Divide each side by '-2'. z = 2.5 Simplifying z = 2.5Solution
z = {-7, 2.5}
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