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Simplifying (-1x + 3)(2x + -1) + (-1x + 3)(x + -7) = 0 Reorder the terms: (3 + -1x)(2x + -1) + (-1x + 3)(x + -7) = 0 Reorder the terms: (3 + -1x)(-1 + 2x) + (-1x + 3)(x + -7) = 0 Multiply (3 + -1x) * (-1 + 2x) (3(-1 + 2x) + -1x * (-1 + 2x)) + (-1x + 3)(x + -7) = 0 ((-1 * 3 + 2x * 3) + -1x * (-1 + 2x)) + (-1x + 3)(x + -7) = 0 ((-3 + 6x) + -1x * (-1 + 2x)) + (-1x + 3)(x + -7) = 0 (-3 + 6x + (-1 * -1x + 2x * -1x)) + (-1x + 3)(x + -7) = 0 (-3 + 6x + (1x + -2x2)) + (-1x + 3)(x + -7) = 0 Combine like terms: 6x + 1x = 7x (-3 + 7x + -2x2) + (-1x + 3)(x + -7) = 0 Reorder the terms: -3 + 7x + -2x2 + (3 + -1x)(x + -7) = 0 Reorder the terms: -3 + 7x + -2x2 + (3 + -1x)(-7 + x) = 0 Multiply (3 + -1x) * (-7 + x) -3 + 7x + -2x2 + (3(-7 + x) + -1x * (-7 + x)) = 0 -3 + 7x + -2x2 + ((-7 * 3 + x * 3) + -1x * (-7 + x)) = 0 -3 + 7x + -2x2 + ((-21 + 3x) + -1x * (-7 + x)) = 0 -3 + 7x + -2x2 + (-21 + 3x + (-7 * -1x + x * -1x)) = 0 -3 + 7x + -2x2 + (-21 + 3x + (7x + -1x2)) = 0 Combine like terms: 3x + 7x = 10x -3 + 7x + -2x2 + (-21 + 10x + -1x2) = 0 Reorder the terms: -3 + -21 + 7x + 10x + -2x2 + -1x2 = 0 Combine like terms: -3 + -21 = -24 -24 + 7x + 10x + -2x2 + -1x2 = 0 Combine like terms: 7x + 10x = 17x -24 + 17x + -2x2 + -1x2 = 0 Combine like terms: -2x2 + -1x2 = -3x2 -24 + 17x + -3x2 = 0 Solving -24 + 17x + -3x2 = 0 Solving for variable 'x'. Factor a trinomial. (-3 + x)(8 + -3x) = 0Subproblem 1
Set the factor '(-3 + x)' equal to zero and attempt to solve: Simplifying -3 + x = 0 Solving -3 + x = 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 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Simplifying x = 3Subproblem 2
Set the factor '(8 + -3x)' equal to zero and attempt to solve: Simplifying 8 + -3x = 0 Solving 8 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -3x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3x = 0 + -8 -3x = 0 + -8 Combine like terms: 0 + -8 = -8 -3x = -8 Divide each side by '-3'. x = 2.666666667 Simplifying x = 2.666666667Solution
x = {3, 2.666666667}
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