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Simplifying (z + -3)(4z + 7) = 0 Reorder the terms: (-3 + z)(4z + 7) = 0 Reorder the terms: (-3 + z)(7 + 4z) = 0 Multiply (-3 + z) * (7 + 4z) (-3(7 + 4z) + z(7 + 4z)) = 0 ((7 * -3 + 4z * -3) + z(7 + 4z)) = 0 ((-21 + -12z) + z(7 + 4z)) = 0 (-21 + -12z + (7 * z + 4z * z)) = 0 (-21 + -12z + (7z + 4z2)) = 0 Combine like terms: -12z + 7z = -5z (-21 + -5z + 4z2) = 0 Solving -21 + -5z + 4z2 = 0 Solving for variable 'z'. Factor a trinomial. (-7 + -4z)(3 + -1z) = 0Subproblem 1
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 = -1.75Subproblem 2
Set the factor '(3 + -1z)' equal to zero and attempt to solve: Simplifying 3 + -1z = 0 Solving 3 + -1z = 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 + -1z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1z = 0 + -3 -1z = 0 + -3 Combine like terms: 0 + -3 = -3 -1z = -3 Divide each side by '-1'. z = 3 Simplifying z = 3Solution
z = {-1.75, 3}
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