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Simplifying (2x + 7)(3x + -2) = 0 Reorder the terms: (7 + 2x)(3x + -2) = 0 Reorder the terms: (7 + 2x)(-2 + 3x) = 0 Multiply (7 + 2x) * (-2 + 3x) (7(-2 + 3x) + 2x * (-2 + 3x)) = 0 ((-2 * 7 + 3x * 7) + 2x * (-2 + 3x)) = 0 ((-14 + 21x) + 2x * (-2 + 3x)) = 0 (-14 + 21x + (-2 * 2x + 3x * 2x)) = 0 (-14 + 21x + (-4x + 6x2)) = 0 Combine like terms: 21x + -4x = 17x (-14 + 17x + 6x2) = 0 Solving -14 + 17x + 6x2 = 0 Solving for variable 'x'. Factor a trinomial. (-7 + -2x)(2 + -3x) = 0Subproblem 1
Set the factor '(-7 + -2x)' equal to zero and attempt to solve: Simplifying -7 + -2x = 0 Solving -7 + -2x = 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 + -2x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -2x = 0 + 7 -2x = 0 + 7 Combine like terms: 0 + 7 = 7 -2x = 7 Divide each side by '-2'. x = -3.5 Simplifying x = -3.5Subproblem 2
Set the factor '(2 + -3x)' equal to zero and attempt to solve: Simplifying 2 + -3x = 0 Solving 2 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3x = 0 + -2 -3x = 0 + -2 Combine like terms: 0 + -2 = -2 -3x = -2 Divide each side by '-3'. x = 0.6666666667 Simplifying x = 0.6666666667Solution
x = {-3.5, 0.6666666667}
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