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Simplifying (x + 2)(x + -3) + -1(2x + -5)(x + 3) = x(x + -5) Reorder the terms: (2 + x)(x + -3) + -1(2x + -5)(x + 3) = x(x + -5) Reorder the terms: (2 + x)(-3 + x) + -1(2x + -5)(x + 3) = x(x + -5) Multiply (2 + x) * (-3 + x) (2(-3 + x) + x(-3 + x)) + -1(2x + -5)(x + 3) = x(x + -5) ((-3 * 2 + x * 2) + x(-3 + x)) + -1(2x + -5)(x + 3) = x(x + -5) ((-6 + 2x) + x(-3 + x)) + -1(2x + -5)(x + 3) = x(x + -5) (-6 + 2x + (-3 * x + x * x)) + -1(2x + -5)(x + 3) = x(x + -5) (-6 + 2x + (-3x + x2)) + -1(2x + -5)(x + 3) = x(x + -5) Combine like terms: 2x + -3x = -1x (-6 + -1x + x2) + -1(2x + -5)(x + 3) = x(x + -5) Reorder the terms: -6 + -1x + x2 + -1(-5 + 2x)(x + 3) = x(x + -5) Reorder the terms: -6 + -1x + x2 + -1(-5 + 2x)(3 + x) = x(x + -5) Multiply (-5 + 2x) * (3 + x) -6 + -1x + x2 + -1(-5(3 + x) + 2x * (3 + x)) = x(x + -5) -6 + -1x + x2 + -1((3 * -5 + x * -5) + 2x * (3 + x)) = x(x + -5) -6 + -1x + x2 + -1((-15 + -5x) + 2x * (3 + x)) = x(x + -5) -6 + -1x + x2 + -1(-15 + -5x + (3 * 2x + x * 2x)) = x(x + -5) -6 + -1x + x2 + -1(-15 + -5x + (6x + 2x2)) = x(x + -5) Combine like terms: -5x + 6x = 1x -6 + -1x + x2 + -1(-15 + 1x + 2x2) = x(x + -5) -6 + -1x + x2 + (-15 * -1 + 1x * -1 + 2x2 * -1) = x(x + -5) -6 + -1x + x2 + (15 + -1x + -2x2) = x(x + -5) Reorder the terms: -6 + 15 + -1x + -1x + x2 + -2x2 = x(x + -5) Combine like terms: -6 + 15 = 9 9 + -1x + -1x + x2 + -2x2 = x(x + -5) Combine like terms: -1x + -1x = -2x 9 + -2x + x2 + -2x2 = x(x + -5) Combine like terms: x2 + -2x2 = -1x2 9 + -2x + -1x2 = x(x + -5) Reorder the terms: 9 + -2x + -1x2 = x(-5 + x) 9 + -2x + -1x2 = (-5 * x + x * x) 9 + -2x + -1x2 = (-5x + x2) Solving 9 + -2x + -1x2 = -5x + x2 Solving for variable 'x'. Reorder the terms: 9 + -2x + 5x + -1x2 + -1x2 = -5x + x2 + 5x + -1x2 Combine like terms: -2x + 5x = 3x 9 + 3x + -1x2 + -1x2 = -5x + x2 + 5x + -1x2 Combine like terms: -1x2 + -1x2 = -2x2 9 + 3x + -2x2 = -5x + x2 + 5x + -1x2 Reorder the terms: 9 + 3x + -2x2 = -5x + 5x + x2 + -1x2 Combine like terms: -5x + 5x = 0 9 + 3x + -2x2 = 0 + x2 + -1x2 9 + 3x + -2x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 9 + 3x + -2x2 = 0 Factor a trinomial. (3 + -1x)(3 + 2x) = 0Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Subproblem 2
Set the factor '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Divide each side by '2'. x = -1.5 Simplifying x = -1.5Solution
x = {3, -1.5}
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