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Simplifying -2(x + -5) + -5(x + -7) = (-3x + 21)(x + -5) Reorder the terms: -2(-5 + x) + -5(x + -7) = (-3x + 21)(x + -5) (-5 * -2 + x * -2) + -5(x + -7) = (-3x + 21)(x + -5) (10 + -2x) + -5(x + -7) = (-3x + 21)(x + -5) Reorder the terms: 10 + -2x + -5(-7 + x) = (-3x + 21)(x + -5) 10 + -2x + (-7 * -5 + x * -5) = (-3x + 21)(x + -5) 10 + -2x + (35 + -5x) = (-3x + 21)(x + -5) Reorder the terms: 10 + 35 + -2x + -5x = (-3x + 21)(x + -5) Combine like terms: 10 + 35 = 45 45 + -2x + -5x = (-3x + 21)(x + -5) Combine like terms: -2x + -5x = -7x 45 + -7x = (-3x + 21)(x + -5) Reorder the terms: 45 + -7x = (21 + -3x)(x + -5) Reorder the terms: 45 + -7x = (21 + -3x)(-5 + x) Multiply (21 + -3x) * (-5 + x) 45 + -7x = (21(-5 + x) + -3x * (-5 + x)) 45 + -7x = ((-5 * 21 + x * 21) + -3x * (-5 + x)) 45 + -7x = ((-105 + 21x) + -3x * (-5 + x)) 45 + -7x = (-105 + 21x + (-5 * -3x + x * -3x)) 45 + -7x = (-105 + 21x + (15x + -3x2)) Combine like terms: 21x + 15x = 36x 45 + -7x = (-105 + 36x + -3x2) Solving 45 + -7x = -105 + 36x + -3x2 Solving for variable 'x'. Reorder the terms: 45 + 105 + -7x + -36x + 3x2 = -105 + 36x + -3x2 + 105 + -36x + 3x2 Combine like terms: 45 + 105 = 150 150 + -7x + -36x + 3x2 = -105 + 36x + -3x2 + 105 + -36x + 3x2 Combine like terms: -7x + -36x = -43x 150 + -43x + 3x2 = -105 + 36x + -3x2 + 105 + -36x + 3x2 Reorder the terms: 150 + -43x + 3x2 = -105 + 105 + 36x + -36x + -3x2 + 3x2 Combine like terms: -105 + 105 = 0 150 + -43x + 3x2 = 0 + 36x + -36x + -3x2 + 3x2 150 + -43x + 3x2 = 36x + -36x + -3x2 + 3x2 Combine like terms: 36x + -36x = 0 150 + -43x + 3x2 = 0 + -3x2 + 3x2 150 + -43x + 3x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 150 + -43x + 3x2 = 0 Factor a trinomial. (6 + -1x)(25 + -3x) = 0Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Subproblem 2
Set the factor '(25 + -3x)' equal to zero and attempt to solve: Simplifying 25 + -3x = 0 Solving 25 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + -3x = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -3x = 0 + -25 -3x = 0 + -25 Combine like terms: 0 + -25 = -25 -3x = -25 Divide each side by '-3'. x = 8.333333333 Simplifying x = 8.333333333Solution
x = {6, 8.333333333}
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