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Simplifying (3x + 4)(x + 9) = 53x + 29 Reorder the terms: (4 + 3x)(x + 9) = 53x + 29 Reorder the terms: (4 + 3x)(9 + x) = 53x + 29 Multiply (4 + 3x) * (9 + x) (4(9 + x) + 3x * (9 + x)) = 53x + 29 ((9 * 4 + x * 4) + 3x * (9 + x)) = 53x + 29 ((36 + 4x) + 3x * (9 + x)) = 53x + 29 (36 + 4x + (9 * 3x + x * 3x)) = 53x + 29 (36 + 4x + (27x + 3x2)) = 53x + 29 Combine like terms: 4x + 27x = 31x (36 + 31x + 3x2) = 53x + 29 Reorder the terms: 36 + 31x + 3x2 = 29 + 53x Solving 36 + 31x + 3x2 = 29 + 53x Solving for variable 'x'. Reorder the terms: 36 + -29 + 31x + -53x + 3x2 = 29 + 53x + -29 + -53x Combine like terms: 36 + -29 = 7 7 + 31x + -53x + 3x2 = 29 + 53x + -29 + -53x Combine like terms: 31x + -53x = -22x 7 + -22x + 3x2 = 29 + 53x + -29 + -53x Reorder the terms: 7 + -22x + 3x2 = 29 + -29 + 53x + -53x Combine like terms: 29 + -29 = 0 7 + -22x + 3x2 = 0 + 53x + -53x 7 + -22x + 3x2 = 53x + -53x Combine like terms: 53x + -53x = 0 7 + -22x + 3x2 = 0 Factor a trinomial. (1 + -3x)(7 + -1x) = 0Subproblem 1
Set the factor '(1 + -3x)' equal to zero and attempt to solve: Simplifying 1 + -3x = 0 Solving 1 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3x = 0 + -1 -3x = 0 + -1 Combine like terms: 0 + -1 = -1 -3x = -1 Divide each side by '-3'. x = 0.3333333333 Simplifying x = 0.3333333333Subproblem 2
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 = 7Solution
x = {0.3333333333, 7}
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