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Simplifying (3x + -1)(7 + -1x) = 0 Reorder the terms: (-1 + 3x)(7 + -1x) = 0 Multiply (-1 + 3x) * (7 + -1x) (-1(7 + -1x) + 3x * (7 + -1x)) = 0 ((7 * -1 + -1x * -1) + 3x * (7 + -1x)) = 0 ((-7 + 1x) + 3x * (7 + -1x)) = 0 (-7 + 1x + (7 * 3x + -1x * 3x)) = 0 (-7 + 1x + (21x + -3x2)) = 0 Combine like terms: 1x + 21x = 22x (-7 + 22x + -3x2) = 0 Solving -7 + 22x + -3x2 = 0 Solving for variable 'x'. Factor a trinomial. (-7 + x)(1 + -3x) = 0Subproblem 1
Set the factor '(-7 + x)' equal to zero and attempt to solve: Simplifying -7 + x = 0 Solving -7 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + x = 0 + 7 x = 0 + 7 Combine like terms: 0 + 7 = 7 x = 7 Simplifying x = 7Subproblem 2
Set the factor '(1 + -3x)' equal to zero and attempt to solve: Simplifying 1 + -3x = 0 Solving 1 + -3x = 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 + -3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3x = 0 + -1 -3x = 0 + -1 Combine like terms: 0 + -1 = -1 -3x = -1 Divide each side by '-3'. x = 0.3333333333 Simplifying x = 0.3333333333Solution
x = {7, 0.3333333333}
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