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Simplifying (2z + -3)(4z + -7) = 0 Reorder the terms: (-3 + 2z)(4z + -7) = 0 Reorder the terms: (-3 + 2z)(-7 + 4z) = 0 Multiply (-3 + 2z) * (-7 + 4z) (-3(-7 + 4z) + 2z * (-7 + 4z)) = 0 ((-7 * -3 + 4z * -3) + 2z * (-7 + 4z)) = 0 ((21 + -12z) + 2z * (-7 + 4z)) = 0 (21 + -12z + (-7 * 2z + 4z * 2z)) = 0 (21 + -12z + (-14z + 8z2)) = 0 Combine like terms: -12z + -14z = -26z (21 + -26z + 8z2) = 0 Solving 21 + -26z + 8z2 = 0 Solving for variable 'z'. Factor a trinomial. (3 + -2z)(7 + -4z) = 0Subproblem 1
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 = 1.5Subproblem 2
Set the factor '(7 + -4z)' equal to zero and attempt to solve: Simplifying 7 + -4z = 0 Solving 7 + -4z = 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 + -4z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4z = 0 + -7 -4z = 0 + -7 Combine like terms: 0 + -7 = -7 -4z = -7 Divide each side by '-4'. z = 1.75 Simplifying z = 1.75Solution
z = {1.5, 1.75}
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