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Simplifying ax(x + 3) + -1(ax + -1)(x + 5) = 0 Reorder the terms: ax(3 + x) + -1(ax + -1)(x + 5) = 0 (3 * ax + x * ax) + -1(ax + -1)(x + 5) = 0 (3ax + ax2) + -1(ax + -1)(x + 5) = 0 Reorder the terms: 3ax + ax2 + -1(-1 + ax)(x + 5) = 0 Reorder the terms: 3ax + ax2 + -1(-1 + ax)(5 + x) = 0 Multiply (-1 + ax) * (5 + x) 3ax + ax2 + -1(-1(5 + x) + ax(5 + x)) = 0 3ax + ax2 + -1((5 * -1 + x * -1) + ax(5 + x)) = 0 3ax + ax2 + -1((-5 + -1x) + ax(5 + x)) = 0 3ax + ax2 + -1(-5 + -1x + (5 * ax + x * ax)) = 0 3ax + ax2 + -1(-5 + -1x + (5ax + ax2)) = 0 Reorder the terms: 3ax + ax2 + -1(-5 + 5ax + ax2 + -1x) = 0 3ax + ax2 + -1(-5 + 5ax + ax2 + -1x) = 0 3ax + ax2 + (-5 * -1 + 5ax * -1 + ax2 * -1 + -1x * -1) = 0 3ax + ax2 + (5 + -5ax + -1ax2 + 1x) = 0 Reorder the terms: 5 + 3ax + -5ax + ax2 + -1ax2 + 1x = 0 Combine like terms: 3ax + -5ax = -2ax 5 + -2ax + ax2 + -1ax2 + 1x = 0 Combine like terms: ax2 + -1ax2 = 0 5 + -2ax + 0 + 1x = 0 5 + -2ax + 1x = 0 Solving 5 + -2ax + 1x = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -2ax + -5 + 1x = 0 + -5 Reorder the terms: 5 + -5 + -2ax + 1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2ax + 1x = 0 + -5 -2ax + 1x = 0 + -5 Combine like terms: 0 + -5 = -5 -2ax + 1x = -5 Add '-1x' to each side of the equation. -2ax + 1x + -1x = -5 + -1x Combine like terms: 1x + -1x = 0 -2ax + 0 = -5 + -1x -2ax = -5 + -1x Divide each side by '-2x'. a = 2.5x-1 + 0.5 Simplifying a = 2.5x-1 + 0.5 Reorder the terms: a = 0.5 + 2.5x-1
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