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Simplifying (7 + -1z)(4z + -6) = 0 Reorder the terms: (7 + -1z)(-6 + 4z) = 0 Multiply (7 + -1z) * (-6 + 4z) (7(-6 + 4z) + -1z * (-6 + 4z)) = 0 ((-6 * 7 + 4z * 7) + -1z * (-6 + 4z)) = 0 ((-42 + 28z) + -1z * (-6 + 4z)) = 0 (-42 + 28z + (-6 * -1z + 4z * -1z)) = 0 (-42 + 28z + (6z + -4z2)) = 0 Combine like terms: 28z + 6z = 34z (-42 + 34z + -4z2) = 0 Solving -42 + 34z + -4z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '2'. 2(-21 + 17z + -2z2) = 0 Factor a trinomial. 2((-7 + z)(3 + -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 '(3 + -2z)' equal to zero and attempt to solve: Simplifying 3 + -2z = 0 Solving 3 + -2z = 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 + -2z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2z = 0 + -3 -2z = 0 + -3 Combine like terms: 0 + -3 = -3 -2z = -3 Divide each side by '-2'. z = 1.5 Simplifying z = 1.5Solution
z = {7, 1.5}
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