24+(12-5x)(3+x)=22+(8+5x)(5-x)-62

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Solution for 24+(12-5x)(3+x)=22+(8+5x)(5-x)-62 equation: 


Simplifying
24 + (12 + -5x)(3 + x) = 22 + (8 + 5x)(5 + -1x) + -62

Multiply (12 + -5x) * (3 + x)
24 + (12(3 + x) + -5x * (3 + x)) = 22 + (8 + 5x)(5 + -1x) + -62
24 + ((3 * 12 + x * 12) + -5x * (3 + x)) = 22 + (8 + 5x)(5 + -1x) + -62
24 + ((36 + 12x) + -5x * (3 + x)) = 22 + (8 + 5x)(5 + -1x) + -62
24 + (36 + 12x + (3 * -5x + x * -5x)) = 22 + (8 + 5x)(5 + -1x) + -62
24 + (36 + 12x + (-15x + -5x2)) = 22 + (8 + 5x)(5 + -1x) + -62

Combine like terms: 12x + -15x = -3x
24 + (36 + -3x + -5x2) = 22 + (8 + 5x)(5 + -1x) + -62

Combine like terms: 24 + 36 = 60
60 + -3x + -5x2 = 22 + (8 + 5x)(5 + -1x) + -62

Multiply (8 + 5x) * (5 + -1x)
60 + -3x + -5x2 = 22 + (8(5 + -1x) + 5x * (5 + -1x)) + -62
60 + -3x + -5x2 = 22 + ((5 * 8 + -1x * 8) + 5x * (5 + -1x)) + -62
60 + -3x + -5x2 = 22 + ((40 + -8x) + 5x * (5 + -1x)) + -62
60 + -3x + -5x2 = 22 + (40 + -8x + (5 * 5x + -1x * 5x)) + -62
60 + -3x + -5x2 = 22 + (40 + -8x + (25x + -5x2)) + -62

Combine like terms: -8x + 25x = 17x
60 + -3x + -5x2 = 22 + (40 + 17x + -5x2) + -62

Reorder the terms:
60 + -3x + -5x2 = 22 + 40 + -62 + 17x + -5x2

Combine like terms: 22 + 40 = 62
60 + -3x + -5x2 = 62 + -62 + 17x + -5x2

Combine like terms: 62 + -62 = 0
60 + -3x + -5x2 = 0 + 17x + -5x2
60 + -3x + -5x2 = 17x + -5x2

Add '5x2' to each side of the equation.
60 + -3x + -5x2 + 5x2 = 17x + -5x2 + 5x2

Combine like terms: -5x2 + 5x2 = 0
60 + -3x + 0 = 17x + -5x2 + 5x2
60 + -3x = 17x + -5x2 + 5x2

Combine like terms: -5x2 + 5x2 = 0
60 + -3x = 17x + 0
60 + -3x = 17x

Solving
60 + -3x = 17x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-17x' to each side of the equation.
60 + -3x + -17x = 17x + -17x

Combine like terms: -3x + -17x = -20x
60 + -20x = 17x + -17x

Combine like terms: 17x + -17x = 0
60 + -20x = 0

Add '-60' to each side of the equation.
60 + -60 + -20x = 0 + -60

Combine like terms: 60 + -60 = 0
0 + -20x = 0 + -60
-20x = 0 + -60

Combine like terms: 0 + -60 = -60
-20x = -60

Divide each side by '-20'.
x = 3

Simplifying
x = 3

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