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Simplifying (4x + -1)(15x + -31) = -1(8x + 25) Reorder the terms: (-1 + 4x)(15x + -31) = -1(8x + 25) Reorder the terms: (-1 + 4x)(-31 + 15x) = -1(8x + 25) Multiply (-1 + 4x) * (-31 + 15x) (-1(-31 + 15x) + 4x * (-31 + 15x)) = -1(8x + 25) ((-31 * -1 + 15x * -1) + 4x * (-31 + 15x)) = -1(8x + 25) ((31 + -15x) + 4x * (-31 + 15x)) = -1(8x + 25) (31 + -15x + (-31 * 4x + 15x * 4x)) = -1(8x + 25) (31 + -15x + (-124x + 60x2)) = -1(8x + 25) Combine like terms: -15x + -124x = -139x (31 + -139x + 60x2) = -1(8x + 25) Reorder the terms: 31 + -139x + 60x2 = -1(25 + 8x) 31 + -139x + 60x2 = (25 * -1 + 8x * -1) 31 + -139x + 60x2 = (-25 + -8x) Solving 31 + -139x + 60x2 = -25 + -8x Solving for variable 'x'. Reorder the terms: 31 + 25 + -139x + 8x + 60x2 = -25 + -8x + 25 + 8x Combine like terms: 31 + 25 = 56 56 + -139x + 8x + 60x2 = -25 + -8x + 25 + 8x Combine like terms: -139x + 8x = -131x 56 + -131x + 60x2 = -25 + -8x + 25 + 8x Reorder the terms: 56 + -131x + 60x2 = -25 + 25 + -8x + 8x Combine like terms: -25 + 25 = 0 56 + -131x + 60x2 = 0 + -8x + 8x 56 + -131x + 60x2 = -8x + 8x Combine like terms: -8x + 8x = 0 56 + -131x + 60x2 = 0 Factor a trinomial. (7 + -12x)(8 + -5x) = 0Subproblem 1
Set the factor '(7 + -12x)' equal to zero and attempt to solve: Simplifying 7 + -12x = 0 Solving 7 + -12x = 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 + -12x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -12x = 0 + -7 -12x = 0 + -7 Combine like terms: 0 + -7 = -7 -12x = -7 Divide each side by '-12'. x = 0.5833333333 Simplifying x = 0.5833333333Subproblem 2
Set the factor '(8 + -5x)' equal to zero and attempt to solve: Simplifying 8 + -5x = 0 Solving 8 + -5x = 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 + -5x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -5x = 0 + -8 -5x = 0 + -8 Combine like terms: 0 + -8 = -8 -5x = -8 Divide each side by '-5'. x = 1.6 Simplifying x = 1.6Solution
x = {0.5833333333, 1.6}
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