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Simplifying (7 + z)(5z + -3) = 0 Reorder the terms: (7 + z)(-3 + 5z) = 0 Multiply (7 + z) * (-3 + 5z) (7(-3 + 5z) + z(-3 + 5z)) = 0 ((-3 * 7 + 5z * 7) + z(-3 + 5z)) = 0 ((-21 + 35z) + z(-3 + 5z)) = 0 (-21 + 35z + (-3 * z + 5z * z)) = 0 (-21 + 35z + (-3z + 5z2)) = 0 Combine like terms: 35z + -3z = 32z (-21 + 32z + 5z2) = 0 Solving -21 + 32z + 5z2 = 0 Solving for variable 'z'. Factor a trinomial. (-7 + -1z)(3 + -5z) = 0Subproblem 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 + -5z)' equal to zero and attempt to solve: Simplifying 3 + -5z = 0 Solving 3 + -5z = 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 + -5z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5z = 0 + -3 -5z = 0 + -3 Combine like terms: 0 + -3 = -3 -5z = -3 Divide each side by '-5'. z = 0.6 Simplifying z = 0.6Solution
z = {-7, 0.6}
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