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Simplifying (4x + -3)(x + -5) = (x + -4)(5x + 3) Reorder the terms: (-3 + 4x)(x + -5) = (x + -4)(5x + 3) Reorder the terms: (-3 + 4x)(-5 + x) = (x + -4)(5x + 3) Multiply (-3 + 4x) * (-5 + x) (-3(-5 + x) + 4x * (-5 + x)) = (x + -4)(5x + 3) ((-5 * -3 + x * -3) + 4x * (-5 + x)) = (x + -4)(5x + 3) ((15 + -3x) + 4x * (-5 + x)) = (x + -4)(5x + 3) (15 + -3x + (-5 * 4x + x * 4x)) = (x + -4)(5x + 3) (15 + -3x + (-20x + 4x2)) = (x + -4)(5x + 3) Combine like terms: -3x + -20x = -23x (15 + -23x + 4x2) = (x + -4)(5x + 3) Reorder the terms: 15 + -23x + 4x2 = (-4 + x)(5x + 3) Reorder the terms: 15 + -23x + 4x2 = (-4 + x)(3 + 5x) Multiply (-4 + x) * (3 + 5x) 15 + -23x + 4x2 = (-4(3 + 5x) + x(3 + 5x)) 15 + -23x + 4x2 = ((3 * -4 + 5x * -4) + x(3 + 5x)) 15 + -23x + 4x2 = ((-12 + -20x) + x(3 + 5x)) 15 + -23x + 4x2 = (-12 + -20x + (3 * x + 5x * x)) 15 + -23x + 4x2 = (-12 + -20x + (3x + 5x2)) Combine like terms: -20x + 3x = -17x 15 + -23x + 4x2 = (-12 + -17x + 5x2) Solving 15 + -23x + 4x2 = -12 + -17x + 5x2 Solving for variable 'x'. Reorder the terms: 15 + 12 + -23x + 17x + 4x2 + -5x2 = -12 + -17x + 5x2 + 12 + 17x + -5x2 Combine like terms: 15 + 12 = 27 27 + -23x + 17x + 4x2 + -5x2 = -12 + -17x + 5x2 + 12 + 17x + -5x2 Combine like terms: -23x + 17x = -6x 27 + -6x + 4x2 + -5x2 = -12 + -17x + 5x2 + 12 + 17x + -5x2 Combine like terms: 4x2 + -5x2 = -1x2 27 + -6x + -1x2 = -12 + -17x + 5x2 + 12 + 17x + -5x2 Reorder the terms: 27 + -6x + -1x2 = -12 + 12 + -17x + 17x + 5x2 + -5x2 Combine like terms: -12 + 12 = 0 27 + -6x + -1x2 = 0 + -17x + 17x + 5x2 + -5x2 27 + -6x + -1x2 = -17x + 17x + 5x2 + -5x2 Combine like terms: -17x + 17x = 0 27 + -6x + -1x2 = 0 + 5x2 + -5x2 27 + -6x + -1x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 27 + -6x + -1x2 = 0 Factor a trinomial. (3 + -1x)(9 + x) = 0Subproblem 1
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 = 3Subproblem 2
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 = -9Solution
x = {3, -9}
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