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Simplifying (6x + 7)(3x + -7) = 0 Reorder the terms: (7 + 6x)(3x + -7) = 0 Reorder the terms: (7 + 6x)(-7 + 3x) = 0 Multiply (7 + 6x) * (-7 + 3x) (7(-7 + 3x) + 6x * (-7 + 3x)) = 0 ((-7 * 7 + 3x * 7) + 6x * (-7 + 3x)) = 0 ((-49 + 21x) + 6x * (-7 + 3x)) = 0 (-49 + 21x + (-7 * 6x + 3x * 6x)) = 0 (-49 + 21x + (-42x + 18x2)) = 0 Combine like terms: 21x + -42x = -21x (-49 + -21x + 18x2) = 0 Solving -49 + -21x + 18x2 = 0 Solving for variable 'x'. Factor a trinomial. (-7 + -6x)(7 + -3x) = 0Subproblem 1
Set the factor '(-7 + -6x)' equal to zero and attempt to solve: Simplifying -7 + -6x = 0 Solving -7 + -6x = 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 + -6x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -6x = 0 + 7 -6x = 0 + 7 Combine like terms: 0 + 7 = 7 -6x = 7 Divide each side by '-6'. x = -1.166666667 Simplifying x = -1.166666667Subproblem 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 = {-1.166666667, 2.333333333}
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