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Simplifying (x + a)(x + -1b) + -1x(x + a) = 0 Reorder the terms: (a + x)(x + -1b) + -1x(x + a) = 0 Reorder the terms: (a + x)(-1b + x) + -1x(x + a) = 0 Multiply (a + x) * (-1b + x) (a(-1b + x) + x(-1b + x)) + -1x(x + a) = 0 ((-1b * a + x * a) + x(-1b + x)) + -1x(x + a) = 0 ((-1ab + ax) + x(-1b + x)) + -1x(x + a) = 0 (-1ab + ax + (-1b * x + x * x)) + -1x(x + a) = 0 (-1ab + ax + (-1bx + x2)) + -1x(x + a) = 0 (-1ab + ax + -1bx + x2) + -1x(x + a) = 0 Reorder the terms: -1ab + ax + -1bx + x2 + -1x(a + x) = 0 -1ab + ax + -1bx + x2 + (a * -1x + x * -1x) = 0 -1ab + ax + -1bx + x2 + (-1ax + -1x2) = 0 Reorder the terms: -1ab + ax + -1ax + -1bx + x2 + -1x2 = 0 Combine like terms: ax + -1ax = 0 -1ab + 0 + -1bx + x2 + -1x2 = 0 -1ab + -1bx + x2 + -1x2 = 0 Combine like terms: x2 + -1x2 = 0 -1ab + -1bx + 0 = 0 -1ab + -1bx = 0 Solving -1ab + -1bx = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add 'bx' to each side of the equation. -1ab + -1bx + bx = 0 + bx Combine like terms: -1bx + bx = 0 -1ab + 0 = 0 + bx -1ab = 0 + bx Remove the zero: -1ab = bx Divide each side by '-1b'. a = -1x Simplifying a = -1x
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