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Simplifying (7 + x)(3x + -5) = 0 Reorder the terms: (7 + x)(-5 + 3x) = 0 Multiply (7 + x) * (-5 + 3x) (7(-5 + 3x) + x(-5 + 3x)) = 0 ((-5 * 7 + 3x * 7) + x(-5 + 3x)) = 0 ((-35 + 21x) + x(-5 + 3x)) = 0 (-35 + 21x + (-5 * x + 3x * x)) = 0 (-35 + 21x + (-5x + 3x2)) = 0 Combine like terms: 21x + -5x = 16x (-35 + 16x + 3x2) = 0 Solving -35 + 16x + 3x2 = 0 Solving for variable 'x'. Factor a trinomial. (-7 + -1x)(5 + -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 '(5 + -3x)' equal to zero and attempt to solve: Simplifying 5 + -3x = 0 Solving 5 + -3x = 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 + -3x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3x = 0 + -5 -3x = 0 + -5 Combine like terms: 0 + -5 = -5 -3x = -5 Divide each side by '-3'. x = 1.666666667 Simplifying x = 1.666666667Solution
x = {-7, 1.666666667}
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