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Simplifying (7 + -1z)(4z + -2) = 0 Reorder the terms: (7 + -1z)(-2 + 4z) = 0 Multiply (7 + -1z) * (-2 + 4z) (7(-2 + 4z) + -1z * (-2 + 4z)) = 0 ((-2 * 7 + 4z * 7) + -1z * (-2 + 4z)) = 0 ((-14 + 28z) + -1z * (-2 + 4z)) = 0 (-14 + 28z + (-2 * -1z + 4z * -1z)) = 0 (-14 + 28z + (2z + -4z2)) = 0 Combine like terms: 28z + 2z = 30z (-14 + 30z + -4z2) = 0 Solving -14 + 30z + -4z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + 15z + -2z2) = 0 Factor a trinomial. 2((-7 + z)(1 + -2z)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + z)' equal to zero and attempt to solve: Simplifying -7 + z = 0 Solving -7 + z = 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 + z = 0 + 7 Combine like terms: -7 + 7 = 0 0 + z = 0 + 7 z = 0 + 7 Combine like terms: 0 + 7 = 7 z = 7 Simplifying z = 7Subproblem 2
Set the factor '(1 + -2z)' equal to zero and attempt to solve: Simplifying 1 + -2z = 0 Solving 1 + -2z = 0 Move all terms containing z to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2z = 0 + -1 -2z = 0 + -1 Combine like terms: 0 + -1 = -1 -2z = -1 Divide each side by '-2'. z = 0.5 Simplifying z = 0.5Solution
z = {7, 0.5}
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