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Simplifying (2x + -3)(x + 4) = 6 Reorder the terms: (-3 + 2x)(x + 4) = 6 Reorder the terms: (-3 + 2x)(4 + x) = 6 Multiply (-3 + 2x) * (4 + x) (-3(4 + x) + 2x * (4 + x)) = 6 ((4 * -3 + x * -3) + 2x * (4 + x)) = 6 ((-12 + -3x) + 2x * (4 + x)) = 6 (-12 + -3x + (4 * 2x + x * 2x)) = 6 (-12 + -3x + (8x + 2x2)) = 6 Combine like terms: -3x + 8x = 5x (-12 + 5x + 2x2) = 6 Solving -12 + 5x + 2x2 = 6 Solving for variable 'x'. Reorder the terms: -12 + -6 + 5x + 2x2 = 6 + -6 Combine like terms: -12 + -6 = -18 -18 + 5x + 2x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -18 + 5x + 2x2 = 0 Factor a trinomial. (-9 + -2x)(2 + -1x) = 0Subproblem 1
Set the factor '(-9 + -2x)' equal to zero and attempt to solve: Simplifying -9 + -2x = 0 Solving -9 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -2x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -2x = 0 + 9 -2x = 0 + 9 Combine like terms: 0 + 9 = 9 -2x = 9 Divide each side by '-2'. x = -4.5 Simplifying x = -4.5Subproblem 2
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 = 2Solution
x = {-4.5, 2}
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