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Simplifying (3x + -5)(x + 3) = (3x + -5)(-3x + -1) Reorder the terms: (-5 + 3x)(x + 3) = (3x + -5)(-3x + -1) Reorder the terms: (-5 + 3x)(3 + x) = (3x + -5)(-3x + -1) Multiply (-5 + 3x) * (3 + x) (-5(3 + x) + 3x * (3 + x)) = (3x + -5)(-3x + -1) ((3 * -5 + x * -5) + 3x * (3 + x)) = (3x + -5)(-3x + -1) ((-15 + -5x) + 3x * (3 + x)) = (3x + -5)(-3x + -1) (-15 + -5x + (3 * 3x + x * 3x)) = (3x + -5)(-3x + -1) (-15 + -5x + (9x + 3x2)) = (3x + -5)(-3x + -1) Combine like terms: -5x + 9x = 4x (-15 + 4x + 3x2) = (3x + -5)(-3x + -1) Reorder the terms: -15 + 4x + 3x2 = (-5 + 3x)(-3x + -1) Reorder the terms: -15 + 4x + 3x2 = (-5 + 3x)(-1 + -3x) Multiply (-5 + 3x) * (-1 + -3x) -15 + 4x + 3x2 = (-5(-1 + -3x) + 3x * (-1 + -3x)) -15 + 4x + 3x2 = ((-1 * -5 + -3x * -5) + 3x * (-1 + -3x)) -15 + 4x + 3x2 = ((5 + 15x) + 3x * (-1 + -3x)) -15 + 4x + 3x2 = (5 + 15x + (-1 * 3x + -3x * 3x)) -15 + 4x + 3x2 = (5 + 15x + (-3x + -9x2)) Combine like terms: 15x + -3x = 12x -15 + 4x + 3x2 = (5 + 12x + -9x2) Solving -15 + 4x + 3x2 = 5 + 12x + -9x2 Solving for variable 'x'. Reorder the terms: -15 + -5 + 4x + -12x + 3x2 + 9x2 = 5 + 12x + -9x2 + -5 + -12x + 9x2 Combine like terms: -15 + -5 = -20 -20 + 4x + -12x + 3x2 + 9x2 = 5 + 12x + -9x2 + -5 + -12x + 9x2 Combine like terms: 4x + -12x = -8x -20 + -8x + 3x2 + 9x2 = 5 + 12x + -9x2 + -5 + -12x + 9x2 Combine like terms: 3x2 + 9x2 = 12x2 -20 + -8x + 12x2 = 5 + 12x + -9x2 + -5 + -12x + 9x2 Reorder the terms: -20 + -8x + 12x2 = 5 + -5 + 12x + -12x + -9x2 + 9x2 Combine like terms: 5 + -5 = 0 -20 + -8x + 12x2 = 0 + 12x + -12x + -9x2 + 9x2 -20 + -8x + 12x2 = 12x + -12x + -9x2 + 9x2 Combine like terms: 12x + -12x = 0 -20 + -8x + 12x2 = 0 + -9x2 + 9x2 -20 + -8x + 12x2 = -9x2 + 9x2 Combine like terms: -9x2 + 9x2 = 0 -20 + -8x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-5 + -2x + 3x2) = 0 Factor a trinomial. 4((-1 + -1x)(5 + -3x)) = 0 Ignore the factor 4.Subproblem 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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