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Simplifying (3x + 7)(x + -4) = 6x + 14 Reorder the terms: (7 + 3x)(x + -4) = 6x + 14 Reorder the terms: (7 + 3x)(-4 + x) = 6x + 14 Multiply (7 + 3x) * (-4 + x) (7(-4 + x) + 3x * (-4 + x)) = 6x + 14 ((-4 * 7 + x * 7) + 3x * (-4 + x)) = 6x + 14 ((-28 + 7x) + 3x * (-4 + x)) = 6x + 14 (-28 + 7x + (-4 * 3x + x * 3x)) = 6x + 14 (-28 + 7x + (-12x + 3x2)) = 6x + 14 Combine like terms: 7x + -12x = -5x (-28 + -5x + 3x2) = 6x + 14 Reorder the terms: -28 + -5x + 3x2 = 14 + 6x Solving -28 + -5x + 3x2 = 14 + 6x Solving for variable 'x'. Reorder the terms: -28 + -14 + -5x + -6x + 3x2 = 14 + 6x + -14 + -6x Combine like terms: -28 + -14 = -42 -42 + -5x + -6x + 3x2 = 14 + 6x + -14 + -6x Combine like terms: -5x + -6x = -11x -42 + -11x + 3x2 = 14 + 6x + -14 + -6x Reorder the terms: -42 + -11x + 3x2 = 14 + -14 + 6x + -6x Combine like terms: 14 + -14 = 0 -42 + -11x + 3x2 = 0 + 6x + -6x -42 + -11x + 3x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -42 + -11x + 3x2 = 0 Factor a trinomial. (-7 + -3x)(6 + -1x) = 0Subproblem 1
Set the factor '(-7 + -3x)' equal to zero and attempt to solve: Simplifying -7 + -3x = 0 Solving -7 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -3x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -3x = 0 + 7 -3x = 0 + 7 Combine like terms: 0 + 7 = 7 -3x = 7 Divide each side by '-3'. x = -2.333333333 Simplifying x = -2.333333333Subproblem 2
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 = 6Solution
x = {-2.333333333, 6}
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