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Simplifying (3x + 2)(x + -1) = x + 3 Reorder the terms: (2 + 3x)(x + -1) = x + 3 Reorder the terms: (2 + 3x)(-1 + x) = x + 3 Multiply (2 + 3x) * (-1 + x) (2(-1 + x) + 3x * (-1 + x)) = x + 3 ((-1 * 2 + x * 2) + 3x * (-1 + x)) = x + 3 ((-2 + 2x) + 3x * (-1 + x)) = x + 3 (-2 + 2x + (-1 * 3x + x * 3x)) = x + 3 (-2 + 2x + (-3x + 3x2)) = x + 3 Combine like terms: 2x + -3x = -1x (-2 + -1x + 3x2) = x + 3 Reorder the terms: -2 + -1x + 3x2 = 3 + x Solving -2 + -1x + 3x2 = 3 + x Solving for variable 'x'. Reorder the terms: -2 + -3 + -1x + -1x + 3x2 = 3 + x + -3 + -1x Combine like terms: -2 + -3 = -5 -5 + -1x + -1x + 3x2 = 3 + x + -3 + -1x Combine like terms: -1x + -1x = -2x -5 + -2x + 3x2 = 3 + x + -3 + -1x Reorder the terms: -5 + -2x + 3x2 = 3 + -3 + x + -1x Combine like terms: 3 + -3 = 0 -5 + -2x + 3x2 = 0 + x + -1x -5 + -2x + 3x2 = x + -1x Combine like terms: x + -1x = 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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