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Simplifying (3 + 2x)(3x + -2) = 0 Reorder the terms: (3 + 2x)(-2 + 3x) = 0 Multiply (3 + 2x) * (-2 + 3x) (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)) = 0 Combine like terms: 9x + -4x = 5x (-6 + 5x + 6x2) = 0 Solving -6 + 5x + 6x2 = 0 Solving for variable 'x'. Factor a trinomial. (-3 + -2x)(2 + -3x) = 0Subproblem 1
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 = -1.5Subproblem 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 = {-1.5, 0.6666666667}
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