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Simplifying (2x + 1)(6x + -3) = (4x + 2)(-7x + 4) Reorder the terms: (1 + 2x)(6x + -3) = (4x + 2)(-7x + 4) Reorder the terms: (1 + 2x)(-3 + 6x) = (4x + 2)(-7x + 4) Multiply (1 + 2x) * (-3 + 6x) (1(-3 + 6x) + 2x * (-3 + 6x)) = (4x + 2)(-7x + 4) ((-3 * 1 + 6x * 1) + 2x * (-3 + 6x)) = (4x + 2)(-7x + 4) ((-3 + 6x) + 2x * (-3 + 6x)) = (4x + 2)(-7x + 4) (-3 + 6x + (-3 * 2x + 6x * 2x)) = (4x + 2)(-7x + 4) (-3 + 6x + (-6x + 12x2)) = (4x + 2)(-7x + 4) Combine like terms: 6x + -6x = 0 (-3 + 0 + 12x2) = (4x + 2)(-7x + 4) (-3 + 12x2) = (4x + 2)(-7x + 4) Reorder the terms: -3 + 12x2 = (2 + 4x)(-7x + 4) Reorder the terms: -3 + 12x2 = (2 + 4x)(4 + -7x) Multiply (2 + 4x) * (4 + -7x) -3 + 12x2 = (2(4 + -7x) + 4x * (4 + -7x)) -3 + 12x2 = ((4 * 2 + -7x * 2) + 4x * (4 + -7x)) -3 + 12x2 = ((8 + -14x) + 4x * (4 + -7x)) -3 + 12x2 = (8 + -14x + (4 * 4x + -7x * 4x)) -3 + 12x2 = (8 + -14x + (16x + -28x2)) Combine like terms: -14x + 16x = 2x -3 + 12x2 = (8 + 2x + -28x2) Solving -3 + 12x2 = 8 + 2x + -28x2 Solving for variable 'x'. Reorder the terms: -3 + -8 + -2x + 12x2 + 28x2 = 8 + 2x + -28x2 + -8 + -2x + 28x2 Combine like terms: -3 + -8 = -11 -11 + -2x + 12x2 + 28x2 = 8 + 2x + -28x2 + -8 + -2x + 28x2 Combine like terms: 12x2 + 28x2 = 40x2 -11 + -2x + 40x2 = 8 + 2x + -28x2 + -8 + -2x + 28x2 Reorder the terms: -11 + -2x + 40x2 = 8 + -8 + 2x + -2x + -28x2 + 28x2 Combine like terms: 8 + -8 = 0 -11 + -2x + 40x2 = 0 + 2x + -2x + -28x2 + 28x2 -11 + -2x + 40x2 = 2x + -2x + -28x2 + 28x2 Combine like terms: 2x + -2x = 0 -11 + -2x + 40x2 = 0 + -28x2 + 28x2 -11 + -2x + 40x2 = -28x2 + 28x2 Combine like terms: -28x2 + 28x2 = 0 -11 + -2x + 40x2 = 0 Factor a trinomial. (-1 + -2x)(11 + -20x) = 0Subproblem 1
Set the factor '(-1 + -2x)' equal to zero and attempt to solve: Simplifying -1 + -2x = 0 Solving -1 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2x = 0 + 1 -2x = 0 + 1 Combine like terms: 0 + 1 = 1 -2x = 1 Divide each side by '-2'. x = -0.5 Simplifying x = -0.5Subproblem 2
Set the factor '(11 + -20x)' equal to zero and attempt to solve: Simplifying 11 + -20x = 0 Solving 11 + -20x = 0 Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -20x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -20x = 0 + -11 -20x = 0 + -11 Combine like terms: 0 + -11 = -11 -20x = -11 Divide each side by '-20'. x = 0.55 Simplifying x = 0.55Solution
x = {-0.5, 0.55}
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