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Simplifying (2X + -1)(3X + -4) = (X + 4)(X + 3) Reorder the terms: (-1 + 2X)(3X + -4) = (X + 4)(X + 3) Reorder the terms: (-1 + 2X)(-4 + 3X) = (X + 4)(X + 3) Multiply (-1 + 2X) * (-4 + 3X) (-1(-4 + 3X) + 2X * (-4 + 3X)) = (X + 4)(X + 3) ((-4 * -1 + 3X * -1) + 2X * (-4 + 3X)) = (X + 4)(X + 3) ((4 + -3X) + 2X * (-4 + 3X)) = (X + 4)(X + 3) (4 + -3X + (-4 * 2X + 3X * 2X)) = (X + 4)(X + 3) (4 + -3X + (-8X + 6X2)) = (X + 4)(X + 3) Combine like terms: -3X + -8X = -11X (4 + -11X + 6X2) = (X + 4)(X + 3) Reorder the terms: 4 + -11X + 6X2 = (4 + X)(X + 3) Reorder the terms: 4 + -11X + 6X2 = (4 + X)(3 + X) Multiply (4 + X) * (3 + X) 4 + -11X + 6X2 = (4(3 + X) + X(3 + X)) 4 + -11X + 6X2 = ((3 * 4 + X * 4) + X(3 + X)) 4 + -11X + 6X2 = ((12 + 4X) + X(3 + X)) 4 + -11X + 6X2 = (12 + 4X + (3 * X + X * X)) 4 + -11X + 6X2 = (12 + 4X + (3X + X2)) Combine like terms: 4X + 3X = 7X 4 + -11X + 6X2 = (12 + 7X + X2) Solving 4 + -11X + 6X2 = 12 + 7X + X2 Solving for variable 'X'. Reorder the terms: 4 + -12 + -11X + -7X + 6X2 + -1X2 = 12 + 7X + X2 + -12 + -7X + -1X2 Combine like terms: 4 + -12 = -8 -8 + -11X + -7X + 6X2 + -1X2 = 12 + 7X + X2 + -12 + -7X + -1X2 Combine like terms: -11X + -7X = -18X -8 + -18X + 6X2 + -1X2 = 12 + 7X + X2 + -12 + -7X + -1X2 Combine like terms: 6X2 + -1X2 = 5X2 -8 + -18X + 5X2 = 12 + 7X + X2 + -12 + -7X + -1X2 Reorder the terms: -8 + -18X + 5X2 = 12 + -12 + 7X + -7X + X2 + -1X2 Combine like terms: 12 + -12 = 0 -8 + -18X + 5X2 = 0 + 7X + -7X + X2 + -1X2 -8 + -18X + 5X2 = 7X + -7X + X2 + -1X2 Combine like terms: 7X + -7X = 0 -8 + -18X + 5X2 = 0 + X2 + -1X2 -8 + -18X + 5X2 = X2 + -1X2 Combine like terms: X2 + -1X2 = 0 -8 + -18X + 5X2 = 0 Factor a trinomial. (-2 + -5X)(4 + -1X) = 0Subproblem 1
Set the factor '(-2 + -5X)' equal to zero and attempt to solve: Simplifying -2 + -5X = 0 Solving -2 + -5X = 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 + -5X = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -5X = 0 + 2 -5X = 0 + 2 Combine like terms: 0 + 2 = 2 -5X = 2 Divide each side by '-5'. X = -0.4 Simplifying X = -0.4Subproblem 2
Set the factor '(4 + -1X)' equal to zero and attempt to solve: Simplifying 4 + -1X = 0 Solving 4 + -1X = 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 + -1X = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1X = 0 + -4 -1X = 0 + -4 Combine like terms: 0 + -4 = -4 -1X = -4 Divide each side by '-1'. X = 4 Simplifying X = 4Solution
X = {-0.4, 4}
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