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Simplifying (7x + -3)(4x + -2) = 2(7x + -3) Reorder the terms: (-3 + 7x)(4x + -2) = 2(7x + -3) Reorder the terms: (-3 + 7x)(-2 + 4x) = 2(7x + -3) Multiply (-3 + 7x) * (-2 + 4x) (-3(-2 + 4x) + 7x * (-2 + 4x)) = 2(7x + -3) ((-2 * -3 + 4x * -3) + 7x * (-2 + 4x)) = 2(7x + -3) ((6 + -12x) + 7x * (-2 + 4x)) = 2(7x + -3) (6 + -12x + (-2 * 7x + 4x * 7x)) = 2(7x + -3) (6 + -12x + (-14x + 28x2)) = 2(7x + -3) Combine like terms: -12x + -14x = -26x (6 + -26x + 28x2) = 2(7x + -3) Reorder the terms: 6 + -26x + 28x2 = 2(-3 + 7x) 6 + -26x + 28x2 = (-3 * 2 + 7x * 2) 6 + -26x + 28x2 = (-6 + 14x) Solving 6 + -26x + 28x2 = -6 + 14x Solving for variable 'x'. Reorder the terms: 6 + 6 + -26x + -14x + 28x2 = -6 + 14x + 6 + -14x Combine like terms: 6 + 6 = 12 12 + -26x + -14x + 28x2 = -6 + 14x + 6 + -14x Combine like terms: -26x + -14x = -40x 12 + -40x + 28x2 = -6 + 14x + 6 + -14x Reorder the terms: 12 + -40x + 28x2 = -6 + 6 + 14x + -14x Combine like terms: -6 + 6 = 0 12 + -40x + 28x2 = 0 + 14x + -14x 12 + -40x + 28x2 = 14x + -14x Combine like terms: 14x + -14x = 0 12 + -40x + 28x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(3 + -10x + 7x2) = 0 Factor a trinomial. 4((3 + -7x)(1 + -1x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(3 + -7x)' equal to zero and attempt to solve: Simplifying 3 + -7x = 0 Solving 3 + -7x = 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 + -7x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -7x = 0 + -3 -7x = 0 + -3 Combine like terms: 0 + -3 = -3 -7x = -3 Divide each side by '-7'. x = 0.4285714286 Simplifying x = 0.4285714286Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {0.4285714286, 1}
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