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Simplifying 5x(a + -6b + 5c) + -2x(b + -1c) = 0 (a * 5x + -6b * 5x + 5c * 5x) + -2x(b + -1c) = 0 (5ax + -30bx + 25cx) + -2x(b + -1c) = 0 5ax + -30bx + 25cx + (b * -2x + -1c * -2x) = 0 5ax + -30bx + 25cx + (-2bx + 2cx) = 0 Reorder the terms: 5ax + -30bx + -2bx + 25cx + 2cx = 0 Combine like terms: -30bx + -2bx = -32bx 5ax + -32bx + 25cx + 2cx = 0 Combine like terms: 25cx + 2cx = 27cx 5ax + -32bx + 27cx = 0 Solving 5ax + -32bx + 27cx = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '32bx' to each side of the equation. 5ax + -32bx + 32bx + 27cx = 0 + 32bx Combine like terms: -32bx + 32bx = 0 5ax + 0 + 27cx = 0 + 32bx 5ax + 27cx = 0 + 32bx Remove the zero: 5ax + 27cx = 32bx Add '-27cx' to each side of the equation. 5ax + 27cx + -27cx = 32bx + -27cx Combine like terms: 27cx + -27cx = 0 5ax + 0 = 32bx + -27cx 5ax = 32bx + -27cx Divide each side by '5x'. a = 6.4b + -5.4c Simplifying a = 6.4b + -5.4c
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