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Simplifying (x + -2)(3x + 5) = (3x + 5)(2x + -3) Reorder the terms: (-2 + x)(3x + 5) = (3x + 5)(2x + -3) Reorder the terms: (-2 + x)(5 + 3x) = (3x + 5)(2x + -3) Multiply (-2 + x) * (5 + 3x) (-2(5 + 3x) + x(5 + 3x)) = (3x + 5)(2x + -3) ((5 * -2 + 3x * -2) + x(5 + 3x)) = (3x + 5)(2x + -3) ((-10 + -6x) + x(5 + 3x)) = (3x + 5)(2x + -3) (-10 + -6x + (5 * x + 3x * x)) = (3x + 5)(2x + -3) (-10 + -6x + (5x + 3x2)) = (3x + 5)(2x + -3) Combine like terms: -6x + 5x = -1x (-10 + -1x + 3x2) = (3x + 5)(2x + -3) Reorder the terms: -10 + -1x + 3x2 = (5 + 3x)(2x + -3) Reorder the terms: -10 + -1x + 3x2 = (5 + 3x)(-3 + 2x) Multiply (5 + 3x) * (-3 + 2x) -10 + -1x + 3x2 = (5(-3 + 2x) + 3x * (-3 + 2x)) -10 + -1x + 3x2 = ((-3 * 5 + 2x * 5) + 3x * (-3 + 2x)) -10 + -1x + 3x2 = ((-15 + 10x) + 3x * (-3 + 2x)) -10 + -1x + 3x2 = (-15 + 10x + (-3 * 3x + 2x * 3x)) -10 + -1x + 3x2 = (-15 + 10x + (-9x + 6x2)) Combine like terms: 10x + -9x = 1x -10 + -1x + 3x2 = (-15 + 1x + 6x2) Solving -10 + -1x + 3x2 = -15 + 1x + 6x2 Solving for variable 'x'. Reorder the terms: -10 + 15 + -1x + -1x + 3x2 + -6x2 = -15 + 1x + 6x2 + 15 + -1x + -6x2 Combine like terms: -10 + 15 = 5 5 + -1x + -1x + 3x2 + -6x2 = -15 + 1x + 6x2 + 15 + -1x + -6x2 Combine like terms: -1x + -1x = -2x 5 + -2x + 3x2 + -6x2 = -15 + 1x + 6x2 + 15 + -1x + -6x2 Combine like terms: 3x2 + -6x2 = -3x2 5 + -2x + -3x2 = -15 + 1x + 6x2 + 15 + -1x + -6x2 Reorder the terms: 5 + -2x + -3x2 = -15 + 15 + 1x + -1x + 6x2 + -6x2 Combine like terms: -15 + 15 = 0 5 + -2x + -3x2 = 0 + 1x + -1x + 6x2 + -6x2 5 + -2x + -3x2 = 1x + -1x + 6x2 + -6x2 Combine like terms: 1x + -1x = 0 5 + -2x + -3x2 = 0 + 6x2 + -6x2 5 + -2x + -3x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 5 + -2x + -3x2 = 0 Factor a trinomial. (1 + -1x)(5 + 3x) = 0Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Subproblem 2
Set the factor '(5 + 3x)' equal to zero and attempt to solve: Simplifying 5 + 3x = 0 Solving 5 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 3x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3x = 0 + -5 3x = 0 + -5 Combine like terms: 0 + -5 = -5 3x = -5 Divide each side by '3'. x = -1.666666667 Simplifying x = -1.666666667Solution
x = {1, -1.666666667}
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