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Simplifying (a + b)(x + -3) + -1(a + b)(x + 1) = 0 Reorder the terms: (a + b)(-3 + x) + -1(a + b)(x + 1) = 0 Multiply (a + b) * (-3 + x) (a(-3 + x) + b(-3 + x)) + -1(a + b)(x + 1) = 0 ((-3 * a + x * a) + b(-3 + x)) + -1(a + b)(x + 1) = 0 ((-3a + ax) + b(-3 + x)) + -1(a + b)(x + 1) = 0 (-3a + ax + (-3 * b + x * b)) + -1(a + b)(x + 1) = 0 (-3a + ax + (-3b + bx)) + -1(a + b)(x + 1) = 0 (-3a + ax + -3b + bx) + -1(a + b)(x + 1) = 0 Reorder the terms: -3a + ax + -3b + bx + -1(a + b)(1 + x) = 0 Multiply (a + b) * (1 + x) -3a + ax + -3b + bx + -1(a(1 + x) + b(1 + x)) = 0 -3a + ax + -3b + bx + -1((1 * a + x * a) + b(1 + x)) = 0 -3a + ax + -3b + bx + -1((1a + ax) + b(1 + x)) = 0 -3a + ax + -3b + bx + -1(1a + ax + (1 * b + x * b)) = 0 -3a + ax + -3b + bx + -1(1a + ax + (1b + bx)) = 0 -3a + ax + -3b + bx + -1(1a + ax + 1b + bx) = 0 -3a + ax + -3b + bx + (1a * -1 + ax * -1 + 1b * -1 + bx * -1) = 0 -3a + ax + -3b + bx + (-1a + -1ax + -1b + -1bx) = 0 Reorder the terms: -3a + -1a + ax + -1ax + -3b + -1b + bx + -1bx = 0 Combine like terms: -3a + -1a = -4a -4a + ax + -1ax + -3b + -1b + bx + -1bx = 0 Combine like terms: ax + -1ax = 0 -4a + 0 + -3b + -1b + bx + -1bx = 0 -4a + -3b + -1b + bx + -1bx = 0 Combine like terms: -3b + -1b = -4b -4a + -4b + bx + -1bx = 0 Combine like terms: bx + -1bx = 0 -4a + -4b + 0 = 0 -4a + -4b = 0 Solving -4a + -4b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4b' to each side of the equation. -4a + -4b + 4b = 0 + 4b Combine like terms: -4b + 4b = 0 -4a + 0 = 0 + 4b -4a = 0 + 4b Remove the zero: -4a = 4b Divide each side by '-4'. a = -1b Simplifying a = -1b
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