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Simplifying (2x + 3)(4x + -3) = 0 Reorder the terms: (3 + 2x)(4x + -3) = 0 Reorder the terms: (3 + 2x)(-3 + 4x) = 0 Multiply (3 + 2x) * (-3 + 4x) (3(-3 + 4x) + 2x * (-3 + 4x)) = 0 ((-3 * 3 + 4x * 3) + 2x * (-3 + 4x)) = 0 ((-9 + 12x) + 2x * (-3 + 4x)) = 0 (-9 + 12x + (-3 * 2x + 4x * 2x)) = 0 (-9 + 12x + (-6x + 8x2)) = 0 Combine like terms: 12x + -6x = 6x (-9 + 6x + 8x2) = 0 Solving -9 + 6x + 8x2 = 0 Solving for variable 'x'. Factor a trinomial. (-3 + -2x)(3 + -4x) = 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 '(3 + -4x)' equal to zero and attempt to solve: Simplifying 3 + -4x = 0 Solving 3 + -4x = 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 + -4x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4x = 0 + -3 -4x = 0 + -3 Combine like terms: 0 + -3 = -3 -4x = -3 Divide each side by '-4'. x = 0.75 Simplifying x = 0.75Solution
x = {-1.5, 0.75}
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