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Simplifying (6x + -3)(5x + 2) = (10x + 1)(2 + 3x) + 1 Reorder the terms: (-3 + 6x)(5x + 2) = (10x + 1)(2 + 3x) + 1 Reorder the terms: (-3 + 6x)(2 + 5x) = (10x + 1)(2 + 3x) + 1 Multiply (-3 + 6x) * (2 + 5x) (-3(2 + 5x) + 6x * (2 + 5x)) = (10x + 1)(2 + 3x) + 1 ((2 * -3 + 5x * -3) + 6x * (2 + 5x)) = (10x + 1)(2 + 3x) + 1 ((-6 + -15x) + 6x * (2 + 5x)) = (10x + 1)(2 + 3x) + 1 (-6 + -15x + (2 * 6x + 5x * 6x)) = (10x + 1)(2 + 3x) + 1 (-6 + -15x + (12x + 30x2)) = (10x + 1)(2 + 3x) + 1 Combine like terms: -15x + 12x = -3x (-6 + -3x + 30x2) = (10x + 1)(2 + 3x) + 1 Reorder the terms: -6 + -3x + 30x2 = (1 + 10x)(2 + 3x) + 1 Multiply (1 + 10x) * (2 + 3x) -6 + -3x + 30x2 = (1(2 + 3x) + 10x * (2 + 3x)) + 1 -6 + -3x + 30x2 = ((2 * 1 + 3x * 1) + 10x * (2 + 3x)) + 1 -6 + -3x + 30x2 = ((2 + 3x) + 10x * (2 + 3x)) + 1 -6 + -3x + 30x2 = (2 + 3x + (2 * 10x + 3x * 10x)) + 1 -6 + -3x + 30x2 = (2 + 3x + (20x + 30x2)) + 1 Combine like terms: 3x + 20x = 23x -6 + -3x + 30x2 = (2 + 23x + 30x2) + 1 Reorder the terms: -6 + -3x + 30x2 = 2 + 1 + 23x + 30x2 Combine like terms: 2 + 1 = 3 -6 + -3x + 30x2 = 3 + 23x + 30x2 Add '-30x2' to each side of the equation. -6 + -3x + 30x2 + -30x2 = 3 + 23x + 30x2 + -30x2 Combine like terms: 30x2 + -30x2 = 0 -6 + -3x + 0 = 3 + 23x + 30x2 + -30x2 -6 + -3x = 3 + 23x + 30x2 + -30x2 Combine like terms: 30x2 + -30x2 = 0 -6 + -3x = 3 + 23x + 0 -6 + -3x = 3 + 23x Solving -6 + -3x = 3 + 23x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-23x' to each side of the equation. -6 + -3x + -23x = 3 + 23x + -23x Combine like terms: -3x + -23x = -26x -6 + -26x = 3 + 23x + -23x Combine like terms: 23x + -23x = 0 -6 + -26x = 3 + 0 -6 + -26x = 3 Add '6' to each side of the equation. -6 + 6 + -26x = 3 + 6 Combine like terms: -6 + 6 = 0 0 + -26x = 3 + 6 -26x = 3 + 6 Combine like terms: 3 + 6 = 9 -26x = 9 Divide each side by '-26'. x = -0.3461538462 Simplifying x = -0.3461538462
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