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Simplifying 3x(x + 4) = (2x + -9)(x + 4) Reorder the terms: 3x(4 + x) = (2x + -9)(x + 4) (4 * 3x + x * 3x) = (2x + -9)(x + 4) (12x + 3x2) = (2x + -9)(x + 4) Reorder the terms: 12x + 3x2 = (-9 + 2x)(x + 4) Reorder the terms: 12x + 3x2 = (-9 + 2x)(4 + x) Multiply (-9 + 2x) * (4 + x) 12x + 3x2 = (-9(4 + x) + 2x * (4 + x)) 12x + 3x2 = ((4 * -9 + x * -9) + 2x * (4 + x)) 12x + 3x2 = ((-36 + -9x) + 2x * (4 + x)) 12x + 3x2 = (-36 + -9x + (4 * 2x + x * 2x)) 12x + 3x2 = (-36 + -9x + (8x + 2x2)) Combine like terms: -9x + 8x = -1x 12x + 3x2 = (-36 + -1x + 2x2) Solving 12x + 3x2 = -36 + -1x + 2x2 Solving for variable 'x'. Reorder the terms: 36 + 12x + x + 3x2 + -2x2 = -36 + -1x + 2x2 + 36 + x + -2x2 Combine like terms: 12x + x = 13x 36 + 13x + 3x2 + -2x2 = -36 + -1x + 2x2 + 36 + x + -2x2 Combine like terms: 3x2 + -2x2 = 1x2 36 + 13x + 1x2 = -36 + -1x + 2x2 + 36 + x + -2x2 Reorder the terms: 36 + 13x + 1x2 = -36 + 36 + -1x + x + 2x2 + -2x2 Combine like terms: -36 + 36 = 0 36 + 13x + 1x2 = 0 + -1x + x + 2x2 + -2x2 36 + 13x + 1x2 = -1x + x + 2x2 + -2x2 Combine like terms: -1x + x = 0 36 + 13x + 1x2 = 0 + 2x2 + -2x2 36 + 13x + 1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 36 + 13x + 1x2 = 0 Factor a trinomial. (9 + x)(4 + x) = 0Subproblem 1
Set the factor '(9 + x)' equal to zero and attempt to solve: Simplifying 9 + x = 0 Solving 9 + x = 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 + x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + x = 0 + -9 x = 0 + -9 Combine like terms: 0 + -9 = -9 x = -9 Simplifying x = -9Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 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 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Solution
x = {-9, -4}
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