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Simplifying 2z(z + 5) + -7(z + 5) = 0 Reorder the terms: 2z(5 + z) + -7(z + 5) = 0 (5 * 2z + z * 2z) + -7(z + 5) = 0 (10z + 2z2) + -7(z + 5) = 0 Reorder the terms: 10z + 2z2 + -7(5 + z) = 0 10z + 2z2 + (5 * -7 + z * -7) = 0 10z + 2z2 + (-35 + -7z) = 0 Reorder the terms: -35 + 10z + -7z + 2z2 = 0 Combine like terms: 10z + -7z = 3z -35 + 3z + 2z2 = 0 Solving -35 + 3z + 2z2 = 0 Solving for variable 'z'. Factor a trinomial. (-5 + -1z)(7 + -2z) = 0Subproblem 1
Set the factor '(-5 + -1z)' equal to zero and attempt to solve: Simplifying -5 + -1z = 0 Solving -5 + -1z = 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 + -1z = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1z = 0 + 5 -1z = 0 + 5 Combine like terms: 0 + 5 = 5 -1z = 5 Divide each side by '-1'. z = -5 Simplifying z = -5Subproblem 2
Set the factor '(7 + -2z)' equal to zero and attempt to solve: Simplifying 7 + -2z = 0 Solving 7 + -2z = 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 + -2z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2z = 0 + -7 -2z = 0 + -7 Combine like terms: 0 + -7 = -7 -2z = -7 Divide each side by '-2'. z = 3.5 Simplifying z = 3.5Solution
z = {-5, 3.5}
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