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Simplifying 56z2 + 2z + -30 = 0 Reorder the terms: -30 + 2z + 56z2 = 0 Solving -30 + 2z + 56z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '2'. 2(-15 + z + 28z2) = 0 Factor a trinomial. 2((-3 + -4z)(5 + -7z)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -4z)' equal to zero and attempt to solve: Simplifying -3 + -4z = 0 Solving -3 + -4z = 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 + -4z = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4z = 0 + 3 -4z = 0 + 3 Combine like terms: 0 + 3 = 3 -4z = 3 Divide each side by '-4'. z = -0.75 Simplifying z = -0.75Subproblem 2
Set the factor '(5 + -7z)' equal to zero and attempt to solve: Simplifying 5 + -7z = 0 Solving 5 + -7z = 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 + -7z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -7z = 0 + -5 -7z = 0 + -5 Combine like terms: 0 + -5 = -5 -7z = -5 Divide each side by '-7'. z = 0.7142857143 Simplifying z = 0.7142857143Solution
z = {-0.75, 0.7142857143}
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