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Simplifying (3x + -1)(x + 5) = 4x + 3 Reorder the terms: (-1 + 3x)(x + 5) = 4x + 3 Reorder the terms: (-1 + 3x)(5 + x) = 4x + 3 Multiply (-1 + 3x) * (5 + x) (-1(5 + x) + 3x * (5 + x)) = 4x + 3 ((5 * -1 + x * -1) + 3x * (5 + x)) = 4x + 3 ((-5 + -1x) + 3x * (5 + x)) = 4x + 3 (-5 + -1x + (5 * 3x + x * 3x)) = 4x + 3 (-5 + -1x + (15x + 3x2)) = 4x + 3 Combine like terms: -1x + 15x = 14x (-5 + 14x + 3x2) = 4x + 3 Reorder the terms: -5 + 14x + 3x2 = 3 + 4x Solving -5 + 14x + 3x2 = 3 + 4x Solving for variable 'x'. Reorder the terms: -5 + -3 + 14x + -4x + 3x2 = 3 + 4x + -3 + -4x Combine like terms: -5 + -3 = -8 -8 + 14x + -4x + 3x2 = 3 + 4x + -3 + -4x Combine like terms: 14x + -4x = 10x -8 + 10x + 3x2 = 3 + 4x + -3 + -4x Reorder the terms: -8 + 10x + 3x2 = 3 + -3 + 4x + -4x Combine like terms: 3 + -3 = 0 -8 + 10x + 3x2 = 0 + 4x + -4x -8 + 10x + 3x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -8 + 10x + 3x2 = 0 Factor a trinomial. (-4 + -1x)(2 + -3x) = 0Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve: Simplifying -4 + -1x = 0 Solving -4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1x = 0 + 4 -1x = 0 + 4 Combine like terms: 0 + 4 = 4 -1x = 4 Divide each side by '-1'. x = -4 Simplifying x = -4Subproblem 2
Set the factor '(2 + -3x)' equal to zero and attempt to solve: Simplifying 2 + -3x = 0 Solving 2 + -3x = 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 + -3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3x = 0 + -2 -3x = 0 + -2 Combine like terms: 0 + -2 = -2 -3x = -2 Divide each side by '-3'. x = 0.6666666667 Simplifying x = 0.6666666667Solution
x = {-4, 0.6666666667}
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