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Simplifying (6x + -1)(2x + 3) = 3(5x + 1) Reorder the terms: (-1 + 6x)(2x + 3) = 3(5x + 1) Reorder the terms: (-1 + 6x)(3 + 2x) = 3(5x + 1) Multiply (-1 + 6x) * (3 + 2x) (-1(3 + 2x) + 6x * (3 + 2x)) = 3(5x + 1) ((3 * -1 + 2x * -1) + 6x * (3 + 2x)) = 3(5x + 1) ((-3 + -2x) + 6x * (3 + 2x)) = 3(5x + 1) (-3 + -2x + (3 * 6x + 2x * 6x)) = 3(5x + 1) (-3 + -2x + (18x + 12x2)) = 3(5x + 1) Combine like terms: -2x + 18x = 16x (-3 + 16x + 12x2) = 3(5x + 1) Reorder the terms: -3 + 16x + 12x2 = 3(1 + 5x) -3 + 16x + 12x2 = (1 * 3 + 5x * 3) -3 + 16x + 12x2 = (3 + 15x) Solving -3 + 16x + 12x2 = 3 + 15x Solving for variable 'x'. Reorder the terms: -3 + -3 + 16x + -15x + 12x2 = 3 + 15x + -3 + -15x Combine like terms: -3 + -3 = -6 -6 + 16x + -15x + 12x2 = 3 + 15x + -3 + -15x Combine like terms: 16x + -15x = 1x -6 + 1x + 12x2 = 3 + 15x + -3 + -15x Reorder the terms: -6 + 1x + 12x2 = 3 + -3 + 15x + -15x Combine like terms: 3 + -3 = 0 -6 + 1x + 12x2 = 0 + 15x + -15x -6 + 1x + 12x2 = 15x + -15x Combine like terms: 15x + -15x = 0 -6 + 1x + 12x2 = 0 Factor a trinomial. (-3 + -4x)(2 + -3x) = 0Subproblem 1
Set the factor '(-3 + -4x)' equal to zero and attempt to solve: Simplifying -3 + -4x = 0 Solving -3 + -4x = 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 + -4x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4x = 0 + 3 -4x = 0 + 3 Combine like terms: 0 + 3 = 3 -4x = 3 Divide each side by '-4'. x = -0.75 Simplifying x = -0.75Subproblem 2
Set the factor '(2 + -3x)' equal to zero and attempt to solve: Simplifying 2 + -3x = 0 Solving 2 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3x = 0 + -2 -3x = 0 + -2 Combine like terms: 0 + -2 = -2 -3x = -2 Divide each side by '-3'. x = 0.6666666667 Simplifying x = 0.6666666667Solution
x = {-0.75, 0.6666666667}
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