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Simplifying 6(3r + -3z) + -4(3z + 8) + 4r = 0 (3r * 6 + -3z * 6) + -4(3z + 8) + 4r = 0 (18r + -18z) + -4(3z + 8) + 4r = 0 Reorder the terms: 18r + -18z + -4(8 + 3z) + 4r = 0 18r + -18z + (8 * -4 + 3z * -4) + 4r = 0 18r + -18z + (-32 + -12z) + 4r = 0 Reorder the terms: -32 + 18r + 4r + -18z + -12z = 0 Combine like terms: 18r + 4r = 22r -32 + 22r + -18z + -12z = 0 Combine like terms: -18z + -12z = -30z -32 + 22r + -30z = 0 Solving -32 + 22r + -30z = 0 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '32' to each side of the equation. -32 + 22r + 32 + -30z = 0 + 32 Reorder the terms: -32 + 32 + 22r + -30z = 0 + 32 Combine like terms: -32 + 32 = 0 0 + 22r + -30z = 0 + 32 22r + -30z = 0 + 32 Combine like terms: 0 + 32 = 32 22r + -30z = 32 Add '30z' to each side of the equation. 22r + -30z + 30z = 32 + 30z Combine like terms: -30z + 30z = 0 22r + 0 = 32 + 30z 22r = 32 + 30z Divide each side by '22'. r = 1.454545455 + 1.363636364z Simplifying r = 1.454545455 + 1.363636364z
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