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Simplifying (2x + -13)(x + -5) = 0 Reorder the terms: (-13 + 2x)(x + -5) = 0 Reorder the terms: (-13 + 2x)(-5 + x) = 0 Multiply (-13 + 2x) * (-5 + x) (-13(-5 + x) + 2x * (-5 + x)) = 0 ((-5 * -13 + x * -13) + 2x * (-5 + x)) = 0 ((65 + -13x) + 2x * (-5 + x)) = 0 (65 + -13x + (-5 * 2x + x * 2x)) = 0 (65 + -13x + (-10x + 2x2)) = 0 Combine like terms: -13x + -10x = -23x (65 + -23x + 2x2) = 0 Solving 65 + -23x + 2x2 = 0 Solving for variable 'x'. Factor a trinomial. (5 + -1x)(13 + -2x) = 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 '(13 + -2x)' equal to zero and attempt to solve: Simplifying 13 + -2x = 0 Solving 13 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -2x = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -2x = 0 + -13 -2x = 0 + -13 Combine like terms: 0 + -13 = -13 -2x = -13 Divide each side by '-2'. x = 6.5 Simplifying x = 6.5Solution
x = {5, 6.5}
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