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Simplifying (2 + -1z)(2z + -7) = 0 Reorder the terms: (2 + -1z)(-7 + 2z) = 0 Multiply (2 + -1z) * (-7 + 2z) (2(-7 + 2z) + -1z * (-7 + 2z)) = 0 ((-7 * 2 + 2z * 2) + -1z * (-7 + 2z)) = 0 ((-14 + 4z) + -1z * (-7 + 2z)) = 0 (-14 + 4z + (-7 * -1z + 2z * -1z)) = 0 (-14 + 4z + (7z + -2z2)) = 0 Combine like terms: 4z + 7z = 11z (-14 + 11z + -2z2) = 0 Solving -14 + 11z + -2z2 = 0 Solving for variable 'z'. Factor a trinomial. (-7 + 2z)(2 + -1z) = 0Subproblem 1
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 = 3.5Subproblem 2
Set the factor '(2 + -1z)' equal to zero and attempt to solve: Simplifying 2 + -1z = 0 Solving 2 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1z = 0 + -2 -1z = 0 + -2 Combine like terms: 0 + -2 = -2 -1z = -2 Divide each side by '-1'. z = 2 Simplifying z = 2Solution
z = {3.5, 2}
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