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Simplifying (6a + -5b + c + -7d) * 7 = 0 Reorder the terms for easier multiplication: 7(6a + -5b + c + -7d) = 0 (6a * 7 + -5b * 7 + c * 7 + -7d * 7) = 0 (42a + -35b + 7c + -49d) = 0 Solving 42a + -35b + 7c + -49d = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '35b' to each side of the equation. 42a + -35b + 7c + 35b + -49d = 0 + 35b Reorder the terms: 42a + -35b + 35b + 7c + -49d = 0 + 35b Combine like terms: -35b + 35b = 0 42a + 0 + 7c + -49d = 0 + 35b 42a + 7c + -49d = 0 + 35b Remove the zero: 42a + 7c + -49d = 35b Add '-7c' to each side of the equation. 42a + 7c + -7c + -49d = 35b + -7c Combine like terms: 7c + -7c = 0 42a + 0 + -49d = 35b + -7c 42a + -49d = 35b + -7c Add '49d' to each side of the equation. 42a + -49d + 49d = 35b + -7c + 49d Combine like terms: -49d + 49d = 0 42a + 0 = 35b + -7c + 49d 42a = 35b + -7c + 49d Divide each side by '42'. a = 0.8333333333b + -0.1666666667c + 1.166666667d Simplifying a = 0.8333333333b + -0.1666666667c + 1.166666667d
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