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Simplifying (7z + -3)(5z + 2) = 0 Reorder the terms: (-3 + 7z)(5z + 2) = 0 Reorder the terms: (-3 + 7z)(2 + 5z) = 0 Multiply (-3 + 7z) * (2 + 5z) (-3(2 + 5z) + 7z * (2 + 5z)) = 0 ((2 * -3 + 5z * -3) + 7z * (2 + 5z)) = 0 ((-6 + -15z) + 7z * (2 + 5z)) = 0 (-6 + -15z + (2 * 7z + 5z * 7z)) = 0 (-6 + -15z + (14z + 35z2)) = 0 Combine like terms: -15z + 14z = -1z (-6 + -1z + 35z2) = 0 Solving -6 + -1z + 35z2 = 0 Solving for variable 'z'. Factor a trinomial. (-2 + -5z)(3 + -7z) = 0Subproblem 1
Set the factor '(-2 + -5z)' equal to zero and attempt to solve: Simplifying -2 + -5z = 0 Solving -2 + -5z = 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 + -5z = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -5z = 0 + 2 -5z = 0 + 2 Combine like terms: 0 + 2 = 2 -5z = 2 Divide each side by '-5'. z = -0.4 Simplifying z = -0.4Subproblem 2
Set the factor '(3 + -7z)' equal to zero and attempt to solve: Simplifying 3 + -7z = 0 Solving 3 + -7z = 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 + -7z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -7z = 0 + -3 -7z = 0 + -3 Combine like terms: 0 + -3 = -3 -7z = -3 Divide each side by '-7'. z = 0.4285714286 Simplifying z = 0.4285714286Solution
z = {-0.4, 0.4285714286}
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