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Simplifying (4 + 3x)(x + 6) = 0 Reorder the terms: (4 + 3x)(6 + x) = 0 Multiply (4 + 3x) * (6 + x) (4(6 + x) + 3x * (6 + x)) = 0 ((6 * 4 + x * 4) + 3x * (6 + x)) = 0 ((24 + 4x) + 3x * (6 + x)) = 0 (24 + 4x + (6 * 3x + x * 3x)) = 0 (24 + 4x + (18x + 3x2)) = 0 Combine like terms: 4x + 18x = 22x (24 + 22x + 3x2) = 0 Solving 24 + 22x + 3x2 = 0 Solving for variable 'x'. Factor a trinomial. (6 + x)(4 + 3x) = 0Subproblem 1
Set the factor '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6Subproblem 2
Set the factor '(4 + 3x)' equal to zero and attempt to solve: Simplifying 4 + 3x = 0 Solving 4 + 3x = 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 + 3x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3x = 0 + -4 3x = 0 + -4 Combine like terms: 0 + -4 = -4 3x = -4 Divide each side by '3'. x = -1.333333333 Simplifying x = -1.333333333Solution
x = {-6, -1.333333333}
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