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Simplifying 2x2 + 10x = (x + 3)(x + 5) Reorder the terms: 10x + 2x2 = (x + 3)(x + 5) Reorder the terms: 10x + 2x2 = (3 + x)(x + 5) Reorder the terms: 10x + 2x2 = (3 + x)(5 + x) Multiply (3 + x) * (5 + x) 10x + 2x2 = (3(5 + x) + x(5 + x)) 10x + 2x2 = ((5 * 3 + x * 3) + x(5 + x)) 10x + 2x2 = ((15 + 3x) + x(5 + x)) 10x + 2x2 = (15 + 3x + (5 * x + x * x)) 10x + 2x2 = (15 + 3x + (5x + x2)) Combine like terms: 3x + 5x = 8x 10x + 2x2 = (15 + 8x + x2) Solving 10x + 2x2 = 15 + 8x + x2 Solving for variable 'x'. Reorder the terms: -15 + 10x + -8x + 2x2 + -1x2 = 15 + 8x + x2 + -15 + -8x + -1x2 Combine like terms: 10x + -8x = 2x -15 + 2x + 2x2 + -1x2 = 15 + 8x + x2 + -15 + -8x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 -15 + 2x + 1x2 = 15 + 8x + x2 + -15 + -8x + -1x2 Reorder the terms: -15 + 2x + 1x2 = 15 + -15 + 8x + -8x + x2 + -1x2 Combine like terms: 15 + -15 = 0 -15 + 2x + 1x2 = 0 + 8x + -8x + x2 + -1x2 -15 + 2x + 1x2 = 8x + -8x + x2 + -1x2 Combine like terms: 8x + -8x = 0 -15 + 2x + 1x2 = 0 + x2 + -1x2 -15 + 2x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -15 + 2x + 1x2 = 0 Factor a trinomial. (-5 + -1x)(3 + -1x) = 0Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve: Simplifying -5 + -1x = 0 Solving -5 + -1x = 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 + -1x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x = 0 + 5 -1x = 0 + 5 Combine like terms: 0 + 5 = 5 -1x = 5 Divide each side by '-1'. x = -5 Simplifying x = -5Subproblem 2
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 = 3Solution
x = {-5, 3}
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