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Simplifying (-4z + -7)(-4z + 3) = 0 Reorder the terms: (-7 + -4z)(-4z + 3) = 0 Reorder the terms: (-7 + -4z)(3 + -4z) = 0 Multiply (-7 + -4z) * (3 + -4z) (-7(3 + -4z) + -4z * (3 + -4z)) = 0 ((3 * -7 + -4z * -7) + -4z * (3 + -4z)) = 0 ((-21 + 28z) + -4z * (3 + -4z)) = 0 (-21 + 28z + (3 * -4z + -4z * -4z)) = 0 (-21 + 28z + (-12z + 16z2)) = 0 Combine like terms: 28z + -12z = 16z (-21 + 16z + 16z2) = 0 Solving -21 + 16z + 16z2 = 0 Solving for variable 'z'. Factor a trinomial. (-7 + -4z)(3 + -4z) = 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 + -4z)' equal to zero and attempt to solve: Simplifying 3 + -4z = 0 Solving 3 + -4z = 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 + -4z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4z = 0 + -3 -4z = 0 + -3 Combine like terms: 0 + -3 = -3 -4z = -3 Divide each side by '-4'. z = 0.75 Simplifying z = 0.75Solution
z = {-1.75, 0.75}
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