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Simplifying 5(4z + 6) + -2(z + -5) = 7z(z + 4) + -1z(7z + -2) + -48 Reorder the terms: 5(6 + 4z) + -2(z + -5) = 7z(z + 4) + -1z(7z + -2) + -48 (6 * 5 + 4z * 5) + -2(z + -5) = 7z(z + 4) + -1z(7z + -2) + -48 (30 + 20z) + -2(z + -5) = 7z(z + 4) + -1z(7z + -2) + -48 Reorder the terms: 30 + 20z + -2(-5 + z) = 7z(z + 4) + -1z(7z + -2) + -48 30 + 20z + (-5 * -2 + z * -2) = 7z(z + 4) + -1z(7z + -2) + -48 30 + 20z + (10 + -2z) = 7z(z + 4) + -1z(7z + -2) + -48 Reorder the terms: 30 + 10 + 20z + -2z = 7z(z + 4) + -1z(7z + -2) + -48 Combine like terms: 30 + 10 = 40 40 + 20z + -2z = 7z(z + 4) + -1z(7z + -2) + -48 Combine like terms: 20z + -2z = 18z 40 + 18z = 7z(z + 4) + -1z(7z + -2) + -48 Reorder the terms: 40 + 18z = 7z(4 + z) + -1z(7z + -2) + -48 40 + 18z = (4 * 7z + z * 7z) + -1z(7z + -2) + -48 40 + 18z = (28z + 7z2) + -1z(7z + -2) + -48 Reorder the terms: 40 + 18z = 28z + 7z2 + -1z(-2 + 7z) + -48 40 + 18z = 28z + 7z2 + (-2 * -1z + 7z * -1z) + -48 40 + 18z = 28z + 7z2 + (2z + -7z2) + -48 Reorder the terms: 40 + 18z = -48 + 28z + 2z + 7z2 + -7z2 Combine like terms: 28z + 2z = 30z 40 + 18z = -48 + 30z + 7z2 + -7z2 Combine like terms: 7z2 + -7z2 = 0 40 + 18z = -48 + 30z + 0 40 + 18z = -48 + 30z Solving 40 + 18z = -48 + 30z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-30z' to each side of the equation. 40 + 18z + -30z = -48 + 30z + -30z Combine like terms: 18z + -30z = -12z 40 + -12z = -48 + 30z + -30z Combine like terms: 30z + -30z = 0 40 + -12z = -48 + 0 40 + -12z = -48 Add '-40' to each side of the equation. 40 + -40 + -12z = -48 + -40 Combine like terms: 40 + -40 = 0 0 + -12z = -48 + -40 -12z = -48 + -40 Combine like terms: -48 + -40 = -88 -12z = -88 Divide each side by '-12'. z = 7.333333333 Simplifying z = 7.333333333
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