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Simplifying (x + 6)(3x + -7) = 0 Reorder the terms: (6 + x)(3x + -7) = 0 Reorder the terms: (6 + x)(-7 + 3x) = 0 Multiply (6 + x) * (-7 + 3x) (6(-7 + 3x) + x(-7 + 3x)) = 0 ((-7 * 6 + 3x * 6) + x(-7 + 3x)) = 0 ((-42 + 18x) + x(-7 + 3x)) = 0 (-42 + 18x + (-7 * x + 3x * x)) = 0 (-42 + 18x + (-7x + 3x2)) = 0 Combine like terms: 18x + -7x = 11x (-42 + 11x + 3x2) = 0 Solving -42 + 11x + 3x2 = 0 Solving for variable 'x'. Factor a trinomial. (-6 + -1x)(7 + -3x) = 0Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve: Simplifying -6 + -1x = 0 Solving -6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1x = 0 + 6 -1x = 0 + 6 Combine like terms: 0 + 6 = 6 -1x = 6 Divide each side by '-1'. x = -6 Simplifying x = -6Subproblem 2
Set the factor '(7 + -3x)' equal to zero and attempt to solve: Simplifying 7 + -3x = 0 Solving 7 + -3x = 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 + -3x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3x = 0 + -7 -3x = 0 + -7 Combine like terms: 0 + -7 = -7 -3x = -7 Divide each side by '-3'. x = 2.333333333 Simplifying x = 2.333333333Solution
x = {-6, 2.333333333}
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