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Simplifying (x + 7)(3x + -1) = 0 Reorder the terms: (7 + x)(3x + -1) = 0 Reorder the terms: (7 + x)(-1 + 3x) = 0 Multiply (7 + x) * (-1 + 3x) (7(-1 + 3x) + x(-1 + 3x)) = 0 ((-1 * 7 + 3x * 7) + x(-1 + 3x)) = 0 ((-7 + 21x) + x(-1 + 3x)) = 0 (-7 + 21x + (-1 * x + 3x * x)) = 0 (-7 + 21x + (-1x + 3x2)) = 0 Combine like terms: 21x + -1x = 20x (-7 + 20x + 3x2) = 0 Solving -7 + 20x + 3x2 = 0 Solving for variable 'x'. Factor a trinomial. (-7 + -1x)(1 + -3x) = 0Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve: Simplifying -7 + -1x = 0 Solving -7 + -1x = 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 + -1x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1x = 0 + 7 -1x = 0 + 7 Combine like terms: 0 + 7 = 7 -1x = 7 Divide each side by '-1'. 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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