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Simplifying (7x + -2)(x + 4) = (3x + 7)(7x + -2) Reorder the terms: (-2 + 7x)(x + 4) = (3x + 7)(7x + -2) Reorder the terms: (-2 + 7x)(4 + x) = (3x + 7)(7x + -2) Multiply (-2 + 7x) * (4 + x) (-2(4 + x) + 7x * (4 + x)) = (3x + 7)(7x + -2) ((4 * -2 + x * -2) + 7x * (4 + x)) = (3x + 7)(7x + -2) ((-8 + -2x) + 7x * (4 + x)) = (3x + 7)(7x + -2) (-8 + -2x + (4 * 7x + x * 7x)) = (3x + 7)(7x + -2) (-8 + -2x + (28x + 7x2)) = (3x + 7)(7x + -2) Combine like terms: -2x + 28x = 26x (-8 + 26x + 7x2) = (3x + 7)(7x + -2) Reorder the terms: -8 + 26x + 7x2 = (7 + 3x)(7x + -2) Reorder the terms: -8 + 26x + 7x2 = (7 + 3x)(-2 + 7x) Multiply (7 + 3x) * (-2 + 7x) -8 + 26x + 7x2 = (7(-2 + 7x) + 3x * (-2 + 7x)) -8 + 26x + 7x2 = ((-2 * 7 + 7x * 7) + 3x * (-2 + 7x)) -8 + 26x + 7x2 = ((-14 + 49x) + 3x * (-2 + 7x)) -8 + 26x + 7x2 = (-14 + 49x + (-2 * 3x + 7x * 3x)) -8 + 26x + 7x2 = (-14 + 49x + (-6x + 21x2)) Combine like terms: 49x + -6x = 43x -8 + 26x + 7x2 = (-14 + 43x + 21x2) Solving -8 + 26x + 7x2 = -14 + 43x + 21x2 Solving for variable 'x'. Reorder the terms: -8 + 14 + 26x + -43x + 7x2 + -21x2 = -14 + 43x + 21x2 + 14 + -43x + -21x2 Combine like terms: -8 + 14 = 6 6 + 26x + -43x + 7x2 + -21x2 = -14 + 43x + 21x2 + 14 + -43x + -21x2 Combine like terms: 26x + -43x = -17x 6 + -17x + 7x2 + -21x2 = -14 + 43x + 21x2 + 14 + -43x + -21x2 Combine like terms: 7x2 + -21x2 = -14x2 6 + -17x + -14x2 = -14 + 43x + 21x2 + 14 + -43x + -21x2 Reorder the terms: 6 + -17x + -14x2 = -14 + 14 + 43x + -43x + 21x2 + -21x2 Combine like terms: -14 + 14 = 0 6 + -17x + -14x2 = 0 + 43x + -43x + 21x2 + -21x2 6 + -17x + -14x2 = 43x + -43x + 21x2 + -21x2 Combine like terms: 43x + -43x = 0 6 + -17x + -14x2 = 0 + 21x2 + -21x2 6 + -17x + -14x2 = 21x2 + -21x2 Combine like terms: 21x2 + -21x2 = 0 6 + -17x + -14x2 = 0 Factor a trinomial. (2 + -7x)(3 + 2x) = 0Subproblem 1
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 = 0.2857142857Subproblem 2
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 = -1.5Solution
x = {0.2857142857, -1.5}
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