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Simplifying (5z + -3)(x + 7) + -1(5z + -3)(x + -6) = 0 Reorder the terms: (-3 + 5z)(x + 7) + -1(5z + -3)(x + -6) = 0 Reorder the terms: (-3 + 5z)(7 + x) + -1(5z + -3)(x + -6) = 0 Multiply (-3 + 5z) * (7 + x) (-3(7 + x) + 5z * (7 + x)) + -1(5z + -3)(x + -6) = 0 ((7 * -3 + x * -3) + 5z * (7 + x)) + -1(5z + -3)(x + -6) = 0 ((-21 + -3x) + 5z * (7 + x)) + -1(5z + -3)(x + -6) = 0 (-21 + -3x + (7 * 5z + x * 5z)) + -1(5z + -3)(x + -6) = 0 Reorder the terms: (-21 + -3x + (5xz + 35z)) + -1(5z + -3)(x + -6) = 0 (-21 + -3x + (5xz + 35z)) + -1(5z + -3)(x + -6) = 0 (-21 + -3x + 5xz + 35z) + -1(5z + -3)(x + -6) = 0 Reorder the terms: -21 + -3x + 5xz + 35z + -1(-3 + 5z)(x + -6) = 0 Reorder the terms: -21 + -3x + 5xz + 35z + -1(-3 + 5z)(-6 + x) = 0 Multiply (-3 + 5z) * (-6 + x) -21 + -3x + 5xz + 35z + -1(-3(-6 + x) + 5z * (-6 + x)) = 0 -21 + -3x + 5xz + 35z + -1((-6 * -3 + x * -3) + 5z * (-6 + x)) = 0 -21 + -3x + 5xz + 35z + -1((18 + -3x) + 5z * (-6 + x)) = 0 -21 + -3x + 5xz + 35z + -1(18 + -3x + (-6 * 5z + x * 5z)) = 0 Reorder the terms: -21 + -3x + 5xz + 35z + -1(18 + -3x + (5xz + -30z)) = 0 -21 + -3x + 5xz + 35z + -1(18 + -3x + (5xz + -30z)) = 0 -21 + -3x + 5xz + 35z + -1(18 + -3x + 5xz + -30z) = 0 -21 + -3x + 5xz + 35z + (18 * -1 + -3x * -1 + 5xz * -1 + -30z * -1) = 0 -21 + -3x + 5xz + 35z + (-18 + 3x + -5xz + 30z) = 0 Reorder the terms: -21 + -18 + -3x + 3x + 5xz + -5xz + 35z + 30z = 0 Combine like terms: -21 + -18 = -39 -39 + -3x + 3x + 5xz + -5xz + 35z + 30z = 0 Combine like terms: -3x + 3x = 0 -39 + 0 + 5xz + -5xz + 35z + 30z = 0 -39 + 5xz + -5xz + 35z + 30z = 0 Combine like terms: 5xz + -5xz = 0 -39 + 0 + 35z + 30z = 0 -39 + 35z + 30z = 0 Combine like terms: 35z + 30z = 65z -39 + 65z = 0 Solving -39 + 65z = 0 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '39' to each side of the equation. -39 + 39 + 65z = 0 + 39 Combine like terms: -39 + 39 = 0 0 + 65z = 0 + 39 65z = 0 + 39 Combine like terms: 0 + 39 = 39 65z = 39 Divide each side by '65'. z = 0.6 Simplifying z = 0.6
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