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Simplifying (x + 4)(3 + -5x) = 6 + -3(x + -1) Reorder the terms: (4 + x)(3 + -5x) = 6 + -3(x + -1) Multiply (4 + x) * (3 + -5x) (4(3 + -5x) + x(3 + -5x)) = 6 + -3(x + -1) ((3 * 4 + -5x * 4) + x(3 + -5x)) = 6 + -3(x + -1) ((12 + -20x) + x(3 + -5x)) = 6 + -3(x + -1) (12 + -20x + (3 * x + -5x * x)) = 6 + -3(x + -1) (12 + -20x + (3x + -5x2)) = 6 + -3(x + -1) Combine like terms: -20x + 3x = -17x (12 + -17x + -5x2) = 6 + -3(x + -1) Reorder the terms: 12 + -17x + -5x2 = 6 + -3(-1 + x) 12 + -17x + -5x2 = 6 + (-1 * -3 + x * -3) 12 + -17x + -5x2 = 6 + (3 + -3x) Combine like terms: 6 + 3 = 9 12 + -17x + -5x2 = 9 + -3x Solving 12 + -17x + -5x2 = 9 + -3x Solving for variable 'x'. Reorder the terms: 12 + -9 + -17x + 3x + -5x2 = 9 + -3x + -9 + 3x Combine like terms: 12 + -9 = 3 3 + -17x + 3x + -5x2 = 9 + -3x + -9 + 3x Combine like terms: -17x + 3x = -14x 3 + -14x + -5x2 = 9 + -3x + -9 + 3x Reorder the terms: 3 + -14x + -5x2 = 9 + -9 + -3x + 3x Combine like terms: 9 + -9 = 0 3 + -14x + -5x2 = 0 + -3x + 3x 3 + -14x + -5x2 = -3x + 3x Combine like terms: -3x + 3x = 0 3 + -14x + -5x2 = 0 Factor a trinomial. (1 + -5x)(3 + x) = 0Subproblem 1
Set the factor '(1 + -5x)' equal to zero and attempt to solve: Simplifying 1 + -5x = 0 Solving 1 + -5x = 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 + -5x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5x = 0 + -1 -5x = 0 + -1 Combine like terms: 0 + -1 = -1 -5x = -1 Divide each side by '-5'. x = 0.2 Simplifying x = 0.2Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Solution
x = {0.2, -3}
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