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Simplifying (3x + -2) + 5(x + -2) = (6x + -1)(6 + -1x) + -1 Reorder the terms: (-2 + 3x) + 5(x + -2) = (6x + -1)(6 + -1x) + -1 Remove parenthesis around (-2 + 3x) -2 + 3x + 5(x + -2) = (6x + -1)(6 + -1x) + -1 Reorder the terms: -2 + 3x + 5(-2 + x) = (6x + -1)(6 + -1x) + -1 -2 + 3x + (-2 * 5 + x * 5) = (6x + -1)(6 + -1x) + -1 -2 + 3x + (-10 + 5x) = (6x + -1)(6 + -1x) + -1 Reorder the terms: -2 + -10 + 3x + 5x = (6x + -1)(6 + -1x) + -1 Combine like terms: -2 + -10 = -12 -12 + 3x + 5x = (6x + -1)(6 + -1x) + -1 Combine like terms: 3x + 5x = 8x -12 + 8x = (6x + -1)(6 + -1x) + -1 Reorder the terms: -12 + 8x = (-1 + 6x)(6 + -1x) + -1 Multiply (-1 + 6x) * (6 + -1x) -12 + 8x = (-1(6 + -1x) + 6x * (6 + -1x)) + -1 -12 + 8x = ((6 * -1 + -1x * -1) + 6x * (6 + -1x)) + -1 -12 + 8x = ((-6 + 1x) + 6x * (6 + -1x)) + -1 -12 + 8x = (-6 + 1x + (6 * 6x + -1x * 6x)) + -1 -12 + 8x = (-6 + 1x + (36x + -6x2)) + -1 Combine like terms: 1x + 36x = 37x -12 + 8x = (-6 + 37x + -6x2) + -1 Reorder the terms: -12 + 8x = -6 + -1 + 37x + -6x2 Combine like terms: -6 + -1 = -7 -12 + 8x = -7 + 37x + -6x2 Solving -12 + 8x = -7 + 37x + -6x2 Solving for variable 'x'. Reorder the terms: -12 + 7 + 8x + -37x + 6x2 = -7 + 37x + -6x2 + 7 + -37x + 6x2 Combine like terms: -12 + 7 = -5 -5 + 8x + -37x + 6x2 = -7 + 37x + -6x2 + 7 + -37x + 6x2 Combine like terms: 8x + -37x = -29x -5 + -29x + 6x2 = -7 + 37x + -6x2 + 7 + -37x + 6x2 Reorder the terms: -5 + -29x + 6x2 = -7 + 7 + 37x + -37x + -6x2 + 6x2 Combine like terms: -7 + 7 = 0 -5 + -29x + 6x2 = 0 + 37x + -37x + -6x2 + 6x2 -5 + -29x + 6x2 = 37x + -37x + -6x2 + 6x2 Combine like terms: 37x + -37x = 0 -5 + -29x + 6x2 = 0 + -6x2 + 6x2 -5 + -29x + 6x2 = -6x2 + 6x2 Combine like terms: -6x2 + 6x2 = 0 -5 + -29x + 6x2 = 0 Factor a trinomial. (-1 + -6x)(5 + -1x) = 0Subproblem 1
Set the factor '(-1 + -6x)' equal to zero and attempt to solve: Simplifying -1 + -6x = 0 Solving -1 + -6x = 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 + -6x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -6x = 0 + 1 -6x = 0 + 1 Combine like terms: 0 + 1 = 1 -6x = 1 Divide each side by '-6'. x = -0.1666666667 Simplifying x = -0.1666666667Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 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 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {-0.1666666667, 5}
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