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Simplifying (7x + -2)(2 + -3x) + (4x + 3)(7x + -2) = 0 Reorder the terms: (-2 + 7x)(2 + -3x) + (4x + 3)(7x + -2) = 0 Multiply (-2 + 7x) * (2 + -3x) (-2(2 + -3x) + 7x * (2 + -3x)) + (4x + 3)(7x + -2) = 0 ((2 * -2 + -3x * -2) + 7x * (2 + -3x)) + (4x + 3)(7x + -2) = 0 ((-4 + 6x) + 7x * (2 + -3x)) + (4x + 3)(7x + -2) = 0 (-4 + 6x + (2 * 7x + -3x * 7x)) + (4x + 3)(7x + -2) = 0 (-4 + 6x + (14x + -21x2)) + (4x + 3)(7x + -2) = 0 Combine like terms: 6x + 14x = 20x (-4 + 20x + -21x2) + (4x + 3)(7x + -2) = 0 Reorder the terms: -4 + 20x + -21x2 + (3 + 4x)(7x + -2) = 0 Reorder the terms: -4 + 20x + -21x2 + (3 + 4x)(-2 + 7x) = 0 Multiply (3 + 4x) * (-2 + 7x) -4 + 20x + -21x2 + (3(-2 + 7x) + 4x * (-2 + 7x)) = 0 -4 + 20x + -21x2 + ((-2 * 3 + 7x * 3) + 4x * (-2 + 7x)) = 0 -4 + 20x + -21x2 + ((-6 + 21x) + 4x * (-2 + 7x)) = 0 -4 + 20x + -21x2 + (-6 + 21x + (-2 * 4x + 7x * 4x)) = 0 -4 + 20x + -21x2 + (-6 + 21x + (-8x + 28x2)) = 0 Combine like terms: 21x + -8x = 13x -4 + 20x + -21x2 + (-6 + 13x + 28x2) = 0 Reorder the terms: -4 + -6 + 20x + 13x + -21x2 + 28x2 = 0 Combine like terms: -4 + -6 = -10 -10 + 20x + 13x + -21x2 + 28x2 = 0 Combine like terms: 20x + 13x = 33x -10 + 33x + -21x2 + 28x2 = 0 Combine like terms: -21x2 + 28x2 = 7x2 -10 + 33x + 7x2 = 0 Solving -10 + 33x + 7x2 = 0 Solving for variable 'x'. Factor a trinomial. (-5 + -1x)(2 + -7x) = 0Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve: Simplifying -5 + -1x = 0 Solving -5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x = 0 + 5 -1x = 0 + 5 Combine like terms: 0 + 5 = 5 -1x = 5 Divide each side by '-1'. x = -5 Simplifying x = -5Subproblem 2
Set the factor '(2 + -7x)' equal to zero and attempt to solve: Simplifying 2 + -7x = 0 Solving 2 + -7x = 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 + -7x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -7x = 0 + -2 -7x = 0 + -2 Combine like terms: 0 + -2 = -2 -7x = -2 Divide each side by '-7'. x = 0.2857142857 Simplifying x = 0.2857142857Solution
x = {-5, 0.2857142857}
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