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Simplifying 3x(x + 3) = (x + 3)(x + 3) Reorder the terms: 3x(3 + x) = (x + 3)(x + 3) (3 * 3x + x * 3x) = (x + 3)(x + 3) (9x + 3x2) = (x + 3)(x + 3) Reorder the terms: 9x + 3x2 = (3 + x)(x + 3) Reorder the terms: 9x + 3x2 = (3 + x)(3 + x) Multiply (3 + x) * (3 + x) 9x + 3x2 = (3(3 + x) + x(3 + x)) 9x + 3x2 = ((3 * 3 + x * 3) + x(3 + x)) 9x + 3x2 = ((9 + 3x) + x(3 + x)) 9x + 3x2 = (9 + 3x + (3 * x + x * x)) 9x + 3x2 = (9 + 3x + (3x + x2)) Combine like terms: 3x + 3x = 6x 9x + 3x2 = (9 + 6x + x2) Solving 9x + 3x2 = 9 + 6x + x2 Solving for variable 'x'. Reorder the terms: -9 + 9x + -6x + 3x2 + -1x2 = 9 + 6x + x2 + -9 + -6x + -1x2 Combine like terms: 9x + -6x = 3x -9 + 3x + 3x2 + -1x2 = 9 + 6x + x2 + -9 + -6x + -1x2 Combine like terms: 3x2 + -1x2 = 2x2 -9 + 3x + 2x2 = 9 + 6x + x2 + -9 + -6x + -1x2 Reorder the terms: -9 + 3x + 2x2 = 9 + -9 + 6x + -6x + x2 + -1x2 Combine like terms: 9 + -9 = 0 -9 + 3x + 2x2 = 0 + 6x + -6x + x2 + -1x2 -9 + 3x + 2x2 = 6x + -6x + x2 + -1x2 Combine like terms: 6x + -6x = 0 -9 + 3x + 2x2 = 0 + x2 + -1x2 -9 + 3x + 2x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -9 + 3x + 2x2 = 0 Factor a trinomial. (-3 + -1x)(3 + -2x) = 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 '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 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 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5Solution
x = {-3, 1.5}
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