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Simplifying 0 = (2x + 3)(3x + -2) Reorder the terms: 0 = (3 + 2x)(3x + -2) Reorder the terms: 0 = (3 + 2x)(-2 + 3x) Multiply (3 + 2x) * (-2 + 3x) 0 = (3(-2 + 3x) + 2x * (-2 + 3x)) 0 = ((-2 * 3 + 3x * 3) + 2x * (-2 + 3x)) 0 = ((-6 + 9x) + 2x * (-2 + 3x)) 0 = (-6 + 9x + (-2 * 2x + 3x * 2x)) 0 = (-6 + 9x + (-4x + 6x2)) Combine like terms: 9x + -4x = 5x 0 = (-6 + 5x + 6x2) Solving 0 = -6 + 5x + 6x2 Solving for variable 'x'. Combine like terms: 0 + 6 = 6 6 + -5x + -6x2 = -6 + 5x + 6x2 + 6 + -5x + -6x2 Reorder the terms: 6 + -5x + -6x2 = -6 + 6 + 5x + -5x + 6x2 + -6x2 Combine like terms: -6 + 6 = 0 6 + -5x + -6x2 = 0 + 5x + -5x + 6x2 + -6x2 6 + -5x + -6x2 = 5x + -5x + 6x2 + -6x2 Combine like terms: 5x + -5x = 0 6 + -5x + -6x2 = 0 + 6x2 + -6x2 6 + -5x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 6 + -5x + -6x2 = 0 Factor a trinomial. (2 + -3x)(3 + 2x) = 0Subproblem 1
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 = 0.6666666667Subproblem 2
Set the factor '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Divide each side by '2'. x = -1.5 Simplifying x = -1.5Solution
x = {0.6666666667, -1.5}
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