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Simplifying (3x + 5)(x + -3) = 6x + 10 Reorder the terms: (5 + 3x)(x + -3) = 6x + 10 Reorder the terms: (5 + 3x)(-3 + x) = 6x + 10 Multiply (5 + 3x) * (-3 + x) (5(-3 + x) + 3x * (-3 + x)) = 6x + 10 ((-3 * 5 + x * 5) + 3x * (-3 + x)) = 6x + 10 ((-15 + 5x) + 3x * (-3 + x)) = 6x + 10 (-15 + 5x + (-3 * 3x + x * 3x)) = 6x + 10 (-15 + 5x + (-9x + 3x2)) = 6x + 10 Combine like terms: 5x + -9x = -4x (-15 + -4x + 3x2) = 6x + 10 Reorder the terms: -15 + -4x + 3x2 = 10 + 6x Solving -15 + -4x + 3x2 = 10 + 6x Solving for variable 'x'. Reorder the terms: -15 + -10 + -4x + -6x + 3x2 = 10 + 6x + -10 + -6x Combine like terms: -15 + -10 = -25 -25 + -4x + -6x + 3x2 = 10 + 6x + -10 + -6x Combine like terms: -4x + -6x = -10x -25 + -10x + 3x2 = 10 + 6x + -10 + -6x Reorder the terms: -25 + -10x + 3x2 = 10 + -10 + 6x + -6x Combine like terms: 10 + -10 = 0 -25 + -10x + 3x2 = 0 + 6x + -6x -25 + -10x + 3x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -25 + -10x + 3x2 = 0 Factor a trinomial. (-5 + -3x)(5 + -1x) = 0Subproblem 1
Set the factor '(-5 + -3x)' equal to zero and attempt to solve: Simplifying -5 + -3x = 0 Solving -5 + -3x = 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 + -3x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -3x = 0 + 5 -3x = 0 + 5 Combine like terms: 0 + 5 = 5 -3x = 5 Divide each side by '-3'. x = -1.666666667 Simplifying x = -1.666666667Subproblem 2
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 = 5Solution
x = {-1.666666667, 5}
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