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Simplifying (2x + 3)(3x + -4) = 0 Reorder the terms: (3 + 2x)(3x + -4) = 0 Reorder the terms: (3 + 2x)(-4 + 3x) = 0 Multiply (3 + 2x) * (-4 + 3x) (3(-4 + 3x) + 2x * (-4 + 3x)) = 0 ((-4 * 3 + 3x * 3) + 2x * (-4 + 3x)) = 0 ((-12 + 9x) + 2x * (-4 + 3x)) = 0 (-12 + 9x + (-4 * 2x + 3x * 2x)) = 0 (-12 + 9x + (-8x + 6x2)) = 0 Combine like terms: 9x + -8x = 1x (-12 + 1x + 6x2) = 0 Solving -12 + 1x + 6x2 = 0 Solving for variable 'x'. Factor a trinomial. (-3 + -2x)(4 + -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 '(4 + -3x)' equal to zero and attempt to solve: Simplifying 4 + -3x = 0 Solving 4 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3x = 0 + -4 -3x = 0 + -4 Combine like terms: 0 + -4 = -4 -3x = -4 Divide each side by '-3'. x = 1.333333333 Simplifying x = 1.333333333Solution
x = {-1.5, 1.333333333}
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