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Simplifying (4x + 3)(x + 3) = (x + 3)(3x + 7) Reorder the terms: (3 + 4x)(x + 3) = (x + 3)(3x + 7) Reorder the terms: (3 + 4x)(3 + x) = (x + 3)(3x + 7) Multiply (3 + 4x) * (3 + x) (3(3 + x) + 4x * (3 + x)) = (x + 3)(3x + 7) ((3 * 3 + x * 3) + 4x * (3 + x)) = (x + 3)(3x + 7) ((9 + 3x) + 4x * (3 + x)) = (x + 3)(3x + 7) (9 + 3x + (3 * 4x + x * 4x)) = (x + 3)(3x + 7) (9 + 3x + (12x + 4x2)) = (x + 3)(3x + 7) Combine like terms: 3x + 12x = 15x (9 + 15x + 4x2) = (x + 3)(3x + 7) Reorder the terms: 9 + 15x + 4x2 = (3 + x)(3x + 7) Reorder the terms: 9 + 15x + 4x2 = (3 + x)(7 + 3x) Multiply (3 + x) * (7 + 3x) 9 + 15x + 4x2 = (3(7 + 3x) + x(7 + 3x)) 9 + 15x + 4x2 = ((7 * 3 + 3x * 3) + x(7 + 3x)) 9 + 15x + 4x2 = ((21 + 9x) + x(7 + 3x)) 9 + 15x + 4x2 = (21 + 9x + (7 * x + 3x * x)) 9 + 15x + 4x2 = (21 + 9x + (7x + 3x2)) Combine like terms: 9x + 7x = 16x 9 + 15x + 4x2 = (21 + 16x + 3x2) Solving 9 + 15x + 4x2 = 21 + 16x + 3x2 Solving for variable 'x'. Reorder the terms: 9 + -21 + 15x + -16x + 4x2 + -3x2 = 21 + 16x + 3x2 + -21 + -16x + -3x2 Combine like terms: 9 + -21 = -12 -12 + 15x + -16x + 4x2 + -3x2 = 21 + 16x + 3x2 + -21 + -16x + -3x2 Combine like terms: 15x + -16x = -1x -12 + -1x + 4x2 + -3x2 = 21 + 16x + 3x2 + -21 + -16x + -3x2 Combine like terms: 4x2 + -3x2 = 1x2 -12 + -1x + 1x2 = 21 + 16x + 3x2 + -21 + -16x + -3x2 Reorder the terms: -12 + -1x + 1x2 = 21 + -21 + 16x + -16x + 3x2 + -3x2 Combine like terms: 21 + -21 = 0 -12 + -1x + 1x2 = 0 + 16x + -16x + 3x2 + -3x2 -12 + -1x + 1x2 = 16x + -16x + 3x2 + -3x2 Combine like terms: 16x + -16x = 0 -12 + -1x + 1x2 = 0 + 3x2 + -3x2 -12 + -1x + 1x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -12 + -1x + 1x2 = 0 Factor a trinomial. (-3 + -1x)(4 + -1x) = 0Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve: Simplifying -3 + -1x = 0 Solving -3 + -1x = 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 + -1x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x = 0 + 3 -1x = 0 + 3 Combine like terms: 0 + 3 = 3 -1x = 3 Divide each side by '-1'. x = -3 Simplifying x = -3Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 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 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {-3, 4}
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