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Simplifying (3x + 11)(x + 7) = 25(x + 7) Reorder the terms: (11 + 3x)(x + 7) = 25(x + 7) Reorder the terms: (11 + 3x)(7 + x) = 25(x + 7) Multiply (11 + 3x) * (7 + x) (11(7 + x) + 3x * (7 + x)) = 25(x + 7) ((7 * 11 + x * 11) + 3x * (7 + x)) = 25(x + 7) ((77 + 11x) + 3x * (7 + x)) = 25(x + 7) (77 + 11x + (7 * 3x + x * 3x)) = 25(x + 7) (77 + 11x + (21x + 3x2)) = 25(x + 7) Combine like terms: 11x + 21x = 32x (77 + 32x + 3x2) = 25(x + 7) Reorder the terms: 77 + 32x + 3x2 = 25(7 + x) 77 + 32x + 3x2 = (7 * 25 + x * 25) 77 + 32x + 3x2 = (175 + 25x) Solving 77 + 32x + 3x2 = 175 + 25x Solving for variable 'x'. Reorder the terms: 77 + -175 + 32x + -25x + 3x2 = 175 + 25x + -175 + -25x Combine like terms: 77 + -175 = -98 -98 + 32x + -25x + 3x2 = 175 + 25x + -175 + -25x Combine like terms: 32x + -25x = 7x -98 + 7x + 3x2 = 175 + 25x + -175 + -25x Reorder the terms: -98 + 7x + 3x2 = 175 + -175 + 25x + -25x Combine like terms: 175 + -175 = 0 -98 + 7x + 3x2 = 0 + 25x + -25x -98 + 7x + 3x2 = 25x + -25x Combine like terms: 25x + -25x = 0 -98 + 7x + 3x2 = 0 Factor a trinomial. (-7 + -1x)(14 + -3x) = 0Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve: Simplifying -7 + -1x = 0 Solving -7 + -1x = 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 + -1x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1x = 0 + 7 -1x = 0 + 7 Combine like terms: 0 + 7 = 7 -1x = 7 Divide each side by '-1'. x = -7 Simplifying x = -7Subproblem 2
Set the factor '(14 + -3x)' equal to zero and attempt to solve: Simplifying 14 + -3x = 0 Solving 14 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + -3x = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -3x = 0 + -14 -3x = 0 + -14 Combine like terms: 0 + -14 = -14 -3x = -14 Divide each side by '-3'. x = 4.666666667 Simplifying x = 4.666666667Solution
x = {-7, 4.666666667}
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