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Simplifying (3x + -5)(3x + 2) = (x + -7)(9x + 1) + 50 Reorder the terms: (-5 + 3x)(3x + 2) = (x + -7)(9x + 1) + 50 Reorder the terms: (-5 + 3x)(2 + 3x) = (x + -7)(9x + 1) + 50 Multiply (-5 + 3x) * (2 + 3x) (-5(2 + 3x) + 3x * (2 + 3x)) = (x + -7)(9x + 1) + 50 ((2 * -5 + 3x * -5) + 3x * (2 + 3x)) = (x + -7)(9x + 1) + 50 ((-10 + -15x) + 3x * (2 + 3x)) = (x + -7)(9x + 1) + 50 (-10 + -15x + (2 * 3x + 3x * 3x)) = (x + -7)(9x + 1) + 50 (-10 + -15x + (6x + 9x2)) = (x + -7)(9x + 1) + 50 Combine like terms: -15x + 6x = -9x (-10 + -9x + 9x2) = (x + -7)(9x + 1) + 50 Reorder the terms: -10 + -9x + 9x2 = (-7 + x)(9x + 1) + 50 Reorder the terms: -10 + -9x + 9x2 = (-7 + x)(1 + 9x) + 50 Multiply (-7 + x) * (1 + 9x) -10 + -9x + 9x2 = (-7(1 + 9x) + x(1 + 9x)) + 50 -10 + -9x + 9x2 = ((1 * -7 + 9x * -7) + x(1 + 9x)) + 50 -10 + -9x + 9x2 = ((-7 + -63x) + x(1 + 9x)) + 50 -10 + -9x + 9x2 = (-7 + -63x + (1 * x + 9x * x)) + 50 -10 + -9x + 9x2 = (-7 + -63x + (1x + 9x2)) + 50 Combine like terms: -63x + 1x = -62x -10 + -9x + 9x2 = (-7 + -62x + 9x2) + 50 Reorder the terms: -10 + -9x + 9x2 = -7 + 50 + -62x + 9x2 Combine like terms: -7 + 50 = 43 -10 + -9x + 9x2 = 43 + -62x + 9x2 Add '-9x2' to each side of the equation. -10 + -9x + 9x2 + -9x2 = 43 + -62x + 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 -10 + -9x + 0 = 43 + -62x + 9x2 + -9x2 -10 + -9x = 43 + -62x + 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 -10 + -9x = 43 + -62x + 0 -10 + -9x = 43 + -62x Solving -10 + -9x = 43 + -62x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '62x' to each side of the equation. -10 + -9x + 62x = 43 + -62x + 62x Combine like terms: -9x + 62x = 53x -10 + 53x = 43 + -62x + 62x Combine like terms: -62x + 62x = 0 -10 + 53x = 43 + 0 -10 + 53x = 43 Add '10' to each side of the equation. -10 + 10 + 53x = 43 + 10 Combine like terms: -10 + 10 = 0 0 + 53x = 43 + 10 53x = 43 + 10 Combine like terms: 43 + 10 = 53 53x = 53 Divide each side by '53'. x = 1 Simplifying x = 1
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