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Simplifying 0 = (3x + 2)(x + -2) Reorder the terms: 0 = (2 + 3x)(x + -2) Reorder the terms: 0 = (2 + 3x)(-2 + x) Multiply (2 + 3x) * (-2 + x) 0 = (2(-2 + x) + 3x * (-2 + x)) 0 = ((-2 * 2 + x * 2) + 3x * (-2 + x)) 0 = ((-4 + 2x) + 3x * (-2 + x)) 0 = (-4 + 2x + (-2 * 3x + x * 3x)) 0 = (-4 + 2x + (-6x + 3x2)) Combine like terms: 2x + -6x = -4x 0 = (-4 + -4x + 3x2) Solving 0 = -4 + -4x + 3x2 Solving for variable 'x'. Combine like terms: 0 + 4 = 4 4 + 4x + -3x2 = -4 + -4x + 3x2 + 4 + 4x + -3x2 Reorder the terms: 4 + 4x + -3x2 = -4 + 4 + -4x + 4x + 3x2 + -3x2 Combine like terms: -4 + 4 = 0 4 + 4x + -3x2 = 0 + -4x + 4x + 3x2 + -3x2 4 + 4x + -3x2 = -4x + 4x + 3x2 + -3x2 Combine like terms: -4x + 4x = 0 4 + 4x + -3x2 = 0 + 3x2 + -3x2 4 + 4x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 4 + 4x + -3x2 = 0 Factor a trinomial. (2 + -1x)(2 + 3x) = 0Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Subproblem 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 = {2, -0.6666666667}
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