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Simplifying (x + 2)(x + 3) = 10x Reorder the terms: (2 + x)(x + 3) = 10x Reorder the terms: (2 + x)(3 + x) = 10x Multiply (2 + x) * (3 + x) (2(3 + x) + x(3 + x)) = 10x ((3 * 2 + x * 2) + x(3 + x)) = 10x ((6 + 2x) + x(3 + x)) = 10x (6 + 2x + (3 * x + x * x)) = 10x (6 + 2x + (3x + x2)) = 10x Combine like terms: 2x + 3x = 5x (6 + 5x + x2) = 10x Solving 6 + 5x + x2 = 10x Solving for variable 'x'. Reorder the terms: 6 + 5x + -10x + x2 = 10x + -10x Combine like terms: 5x + -10x = -5x 6 + -5x + x2 = 10x + -10x Combine like terms: 10x + -10x = 0 6 + -5x + x2 = 0 Factor a trinomial. (2 + -1x)(3 + -1x) = 0Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Subproblem 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 = {2, 3}
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