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Simplifying (4z + -6)(7 + z) = 0 Reorder the terms: (-6 + 4z)(7 + z) = 0 Multiply (-6 + 4z) * (7 + z) (-6(7 + z) + 4z * (7 + z)) = 0 ((7 * -6 + z * -6) + 4z * (7 + z)) = 0 ((-42 + -6z) + 4z * (7 + z)) = 0 (-42 + -6z + (7 * 4z + z * 4z)) = 0 (-42 + -6z + (28z + 4z2)) = 0 Combine like terms: -6z + 28z = 22z (-42 + 22z + 4z2) = 0 Solving -42 + 22z + 4z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '2'. 2(-21 + 11z + 2z2) = 0 Factor a trinomial. 2((-7 + -1z)(3 + -2z)) = 0 Ignore the factor 2.Subproblem 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 '(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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