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Simplifying 5z + 7(z + -5) + -3(y + -5) = 0 Reorder the terms: 5z + 7(-5 + z) + -3(y + -5) = 0 5z + (-5 * 7 + z * 7) + -3(y + -5) = 0 5z + (-35 + 7z) + -3(y + -5) = 0 Reorder the terms: 5z + -35 + 7z + -3(-5 + y) = 0 5z + -35 + 7z + (-5 * -3 + y * -3) = 0 5z + -35 + 7z + (15 + -3y) = 0 Reorder the terms: -35 + 15 + -3y + 5z + 7z = 0 Combine like terms: -35 + 15 = -20 -20 + -3y + 5z + 7z = 0 Combine like terms: 5z + 7z = 12z -20 + -3y + 12z = 0 Solving -20 + -3y + 12z = 0 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '20' to each side of the equation. -20 + -3y + 20 + 12z = 0 + 20 Reorder the terms: -20 + 20 + -3y + 12z = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -3y + 12z = 0 + 20 -3y + 12z = 0 + 20 Combine like terms: 0 + 20 = 20 -3y + 12z = 20 Add '-12z' to each side of the equation. -3y + 12z + -12z = 20 + -12z Combine like terms: 12z + -12z = 0 -3y + 0 = 20 + -12z -3y = 20 + -12z Divide each side by '-3'. y = -6.666666667 + 4z Simplifying y = -6.666666667 + 4z
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