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Simplifying 3x(x + 5) = (2x + -9)(x + 5) Reorder the terms: 3x(5 + x) = (2x + -9)(x + 5) (5 * 3x + x * 3x) = (2x + -9)(x + 5) (15x + 3x2) = (2x + -9)(x + 5) Reorder the terms: 15x + 3x2 = (-9 + 2x)(x + 5) Reorder the terms: 15x + 3x2 = (-9 + 2x)(5 + x) Multiply (-9 + 2x) * (5 + x) 15x + 3x2 = (-9(5 + x) + 2x * (5 + x)) 15x + 3x2 = ((5 * -9 + x * -9) + 2x * (5 + x)) 15x + 3x2 = ((-45 + -9x) + 2x * (5 + x)) 15x + 3x2 = (-45 + -9x + (5 * 2x + x * 2x)) 15x + 3x2 = (-45 + -9x + (10x + 2x2)) Combine like terms: -9x + 10x = 1x 15x + 3x2 = (-45 + 1x + 2x2) Solving 15x + 3x2 = -45 + 1x + 2x2 Solving for variable 'x'. Reorder the terms: 45 + 15x + -1x + 3x2 + -2x2 = -45 + 1x + 2x2 + 45 + -1x + -2x2 Combine like terms: 15x + -1x = 14x 45 + 14x + 3x2 + -2x2 = -45 + 1x + 2x2 + 45 + -1x + -2x2 Combine like terms: 3x2 + -2x2 = 1x2 45 + 14x + 1x2 = -45 + 1x + 2x2 + 45 + -1x + -2x2 Reorder the terms: 45 + 14x + 1x2 = -45 + 45 + 1x + -1x + 2x2 + -2x2 Combine like terms: -45 + 45 = 0 45 + 14x + 1x2 = 0 + 1x + -1x + 2x2 + -2x2 45 + 14x + 1x2 = 1x + -1x + 2x2 + -2x2 Combine like terms: 1x + -1x = 0 45 + 14x + 1x2 = 0 + 2x2 + -2x2 45 + 14x + 1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 45 + 14x + 1x2 = 0 Factor a trinomial. (9 + x)(5 + 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 '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 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 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5Solution
x = {-9, -5}
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