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Simplifying 3(x + 5) + 4x(x + 5) = 0 Reorder the terms: 3(5 + x) + 4x(x + 5) = 0 (5 * 3 + x * 3) + 4x(x + 5) = 0 (15 + 3x) + 4x(x + 5) = 0 Reorder the terms: 15 + 3x + 4x(5 + x) = 0 15 + 3x + (5 * 4x + x * 4x) = 0 15 + 3x + (20x + 4x2) = 0 Combine like terms: 3x + 20x = 23x 15 + 23x + 4x2 = 0 Solving 15 + 23x + 4x2 = 0 Solving for variable 'x'. Factor a trinomial. (5 + x)(3 + 4x) = 0Subproblem 1
Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 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 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5Subproblem 2
Set the factor '(3 + 4x)' equal to zero and attempt to solve: Simplifying 3 + 4x = 0 Solving 3 + 4x = 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 + 4x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4x = 0 + -3 4x = 0 + -3 Combine like terms: 0 + -3 = -3 4x = -3 Divide each side by '4'. x = -0.75 Simplifying x = -0.75Solution
x = {-5, -0.75}
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