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Simplifying (4x + 7)(x + -6) = 8x + 14 Reorder the terms: (7 + 4x)(x + -6) = 8x + 14 Reorder the terms: (7 + 4x)(-6 + x) = 8x + 14 Multiply (7 + 4x) * (-6 + x) (7(-6 + x) + 4x * (-6 + x)) = 8x + 14 ((-6 * 7 + x * 7) + 4x * (-6 + x)) = 8x + 14 ((-42 + 7x) + 4x * (-6 + x)) = 8x + 14 (-42 + 7x + (-6 * 4x + x * 4x)) = 8x + 14 (-42 + 7x + (-24x + 4x2)) = 8x + 14 Combine like terms: 7x + -24x = -17x (-42 + -17x + 4x2) = 8x + 14 Reorder the terms: -42 + -17x + 4x2 = 14 + 8x Solving -42 + -17x + 4x2 = 14 + 8x Solving for variable 'x'. Reorder the terms: -42 + -14 + -17x + -8x + 4x2 = 14 + 8x + -14 + -8x Combine like terms: -42 + -14 = -56 -56 + -17x + -8x + 4x2 = 14 + 8x + -14 + -8x Combine like terms: -17x + -8x = -25x -56 + -25x + 4x2 = 14 + 8x + -14 + -8x Reorder the terms: -56 + -25x + 4x2 = 14 + -14 + 8x + -8x Combine like terms: 14 + -14 = 0 -56 + -25x + 4x2 = 0 + 8x + -8x -56 + -25x + 4x2 = 8x + -8x Combine like terms: 8x + -8x = 0 -56 + -25x + 4x2 = 0 Factor a trinomial. (-7 + -4x)(8 + -1x) = 0Subproblem 1
Set the factor '(-7 + -4x)' equal to zero and attempt to solve: Simplifying -7 + -4x = 0 Solving -7 + -4x = 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 + -4x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -4x = 0 + 7 -4x = 0 + 7 Combine like terms: 0 + 7 = 7 -4x = 7 Divide each side by '-4'. x = -1.75 Simplifying x = -1.75Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Divide each side by '-1'. x = 8 Simplifying x = 8Solution
x = {-1.75, 8}
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