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Simplifying (3x + 5)(4x + 7) = 0 Reorder the terms: (5 + 3x)(4x + 7) = 0 Reorder the terms: (5 + 3x)(7 + 4x) = 0 Multiply (5 + 3x) * (7 + 4x) (5(7 + 4x) + 3x * (7 + 4x)) = 0 ((7 * 5 + 4x * 5) + 3x * (7 + 4x)) = 0 ((35 + 20x) + 3x * (7 + 4x)) = 0 (35 + 20x + (7 * 3x + 4x * 3x)) = 0 (35 + 20x + (21x + 12x2)) = 0 Combine like terms: 20x + 21x = 41x (35 + 41x + 12x2) = 0 Solving 35 + 41x + 12x2 = 0 Solving for variable 'x'. Factor a trinomial. (7 + 4x)(5 + 3x) = 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 '(5 + 3x)' equal to zero and attempt to solve: Simplifying 5 + 3x = 0 Solving 5 + 3x = 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 + 3x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3x = 0 + -5 3x = 0 + -5 Combine like terms: 0 + -5 = -5 3x = -5 Divide each side by '3'. x = -1.666666667 Simplifying x = -1.666666667Solution
x = {-1.75, -1.666666667}
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