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Simplifying (4x + 9)(7 + x) = 0 Reorder the terms: (9 + 4x)(7 + x) = 0 Multiply (9 + 4x) * (7 + x) (9(7 + x) + 4x * (7 + x)) = 0 ((7 * 9 + x * 9) + 4x * (7 + x)) = 0 ((63 + 9x) + 4x * (7 + x)) = 0 (63 + 9x + (7 * 4x + x * 4x)) = 0 (63 + 9x + (28x + 4x2)) = 0 Combine like terms: 9x + 28x = 37x (63 + 37x + 4x2) = 0 Solving 63 + 37x + 4x2 = 0 Solving for variable 'x'. Factor a trinomial. (7 + x)(9 + 4x) = 0Subproblem 1
Set the factor '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 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 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Simplifying x = -7Subproblem 2
Set the factor '(9 + 4x)' equal to zero and attempt to solve: Simplifying 9 + 4x = 0 Solving 9 + 4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 4x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 4x = 0 + -9 4x = 0 + -9 Combine like terms: 0 + -9 = -9 4x = -9 Divide each side by '4'. x = -2.25 Simplifying x = -2.25Solution
x = {-7, -2.25}
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