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Simplifying (x + 10)((6x + 10) + -40) = (x + -5)((6x + 10) + 50) Reorder the terms: (10 + x)((6x + 10) + -40) = (x + -5)((6x + 10) + 50) Reorder the terms: (10 + x)((10 + 6x) + -40) = (x + -5)((6x + 10) + 50) Remove parenthesis around (10 + 6x) (10 + x)(10 + 6x + -40) = (x + -5)((6x + 10) + 50) Reorder the terms: (10 + x)(10 + -40 + 6x) = (x + -5)((6x + 10) + 50) Combine like terms: 10 + -40 = -30 (10 + x)(-30 + 6x) = (x + -5)((6x + 10) + 50) Multiply (10 + x) * (-30 + 6x) (10(-30 + 6x) + x(-30 + 6x)) = (x + -5)((6x + 10) + 50) ((-30 * 10 + 6x * 10) + x(-30 + 6x)) = (x + -5)((6x + 10) + 50) ((-300 + 60x) + x(-30 + 6x)) = (x + -5)((6x + 10) + 50) (-300 + 60x + (-30 * x + 6x * x)) = (x + -5)((6x + 10) + 50) (-300 + 60x + (-30x + 6x2)) = (x + -5)((6x + 10) + 50) Combine like terms: 60x + -30x = 30x (-300 + 30x + 6x2) = (x + -5)((6x + 10) + 50) Reorder the terms: -300 + 30x + 6x2 = (-5 + x)((6x + 10) + 50) Reorder the terms: -300 + 30x + 6x2 = (-5 + x)((10 + 6x) + 50) Remove parenthesis around (10 + 6x) -300 + 30x + 6x2 = (-5 + x)(10 + 6x + 50) Reorder the terms: -300 + 30x + 6x2 = (-5 + x)(10 + 50 + 6x) Combine like terms: 10 + 50 = 60 -300 + 30x + 6x2 = (-5 + x)(60 + 6x) Multiply (-5 + x) * (60 + 6x) -300 + 30x + 6x2 = (-5(60 + 6x) + x(60 + 6x)) -300 + 30x + 6x2 = ((60 * -5 + 6x * -5) + x(60 + 6x)) -300 + 30x + 6x2 = ((-300 + -30x) + x(60 + 6x)) -300 + 30x + 6x2 = (-300 + -30x + (60 * x + 6x * x)) -300 + 30x + 6x2 = (-300 + -30x + (60x + 6x2)) Combine like terms: -30x + 60x = 30x -300 + 30x + 6x2 = (-300 + 30x + 6x2) Add '300' to each side of the equation. -300 + 30x + 300 + 6x2 = -300 + 30x + 300 + 6x2 Reorder the terms: -300 + 300 + 30x + 6x2 = -300 + 30x + 300 + 6x2 Combine like terms: -300 + 300 = 0 0 + 30x + 6x2 = -300 + 30x + 300 + 6x2 30x + 6x2 = -300 + 30x + 300 + 6x2 Reorder the terms: 30x + 6x2 = -300 + 300 + 30x + 6x2 Combine like terms: -300 + 300 = 0 30x + 6x2 = 0 + 30x + 6x2 30x + 6x2 = 30x + 6x2 Add '-30x' to each side of the equation. 30x + -30x + 6x2 = 30x + -30x + 6x2 Combine like terms: 30x + -30x = 0 0 + 6x2 = 30x + -30x + 6x2 6x2 = 30x + -30x + 6x2 Combine like terms: 30x + -30x = 0 6x2 = 0 + 6x2 6x2 = 6x2 Add '-6x2' to each side of the equation. 6x2 + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 0 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 0 = 0 Solving 0 = 0 Couldn't find a variable to solve for. This equation is an identity, all real numbers are solutions.
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