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Simplifying (4x + 7)(7x + 4) = 0 Reorder the terms: (7 + 4x)(7x + 4) = 0 Reorder the terms: (7 + 4x)(4 + 7x) = 0 Multiply (7 + 4x) * (4 + 7x) (7(4 + 7x) + 4x * (4 + 7x)) = 0 ((4 * 7 + 7x * 7) + 4x * (4 + 7x)) = 0 ((28 + 49x) + 4x * (4 + 7x)) = 0 (28 + 49x + (4 * 4x + 7x * 4x)) = 0 (28 + 49x + (16x + 28x2)) = 0 Combine like terms: 49x + 16x = 65x (28 + 65x + 28x2) = 0 Solving 28 + 65x + 28x2 = 0 Solving for variable 'x'. Factor a trinomial. (7 + 4x)(4 + 7x) = 0Subproblem 1
Set the factor '(7 + 4x)' equal to zero and attempt to solve: Simplifying 7 + 4x = 0 Solving 7 + 4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 4x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 4x = 0 + -7 4x = 0 + -7 Combine like terms: 0 + -7 = -7 4x = -7 Divide each side by '4'. x = -1.75 Simplifying x = -1.75Subproblem 2
Set the factor '(4 + 7x)' equal to zero and attempt to solve: Simplifying 4 + 7x = 0 Solving 4 + 7x = 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 + 7x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 7x = 0 + -4 7x = 0 + -4 Combine like terms: 0 + -4 = -4 7x = -4 Divide each side by '7'. x = -0.5714285714 Simplifying x = -0.5714285714Solution
x = {-1.75, -0.5714285714}
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