(x+12)(x+5)=(x-8)(x+7)-10

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Solution for (x+12)(x+5)=(x-8)(x+7)-10 equation: 


Simplifying
(x + 12)(x + 5) = (x + -8)(x + 7) + -10

Reorder the terms:
(12 + x)(x + 5) = (x + -8)(x + 7) + -10

Reorder the terms:
(12 + x)(5 + x) = (x + -8)(x + 7) + -10

Multiply (12 + x) * (5 + x)
(12(5 + x) + x(5 + x)) = (x + -8)(x + 7) + -10
((5 * 12 + x * 12) + x(5 + x)) = (x + -8)(x + 7) + -10
((60 + 12x) + x(5 + x)) = (x + -8)(x + 7) + -10
(60 + 12x + (5 * x + x * x)) = (x + -8)(x + 7) + -10
(60 + 12x + (5x + x2)) = (x + -8)(x + 7) + -10

Combine like terms: 12x + 5x = 17x
(60 + 17x + x2) = (x + -8)(x + 7) + -10

Reorder the terms:
60 + 17x + x2 = (-8 + x)(x + 7) + -10

Reorder the terms:
60 + 17x + x2 = (-8 + x)(7 + x) + -10

Multiply (-8 + x) * (7 + x)
60 + 17x + x2 = (-8(7 + x) + x(7 + x)) + -10
60 + 17x + x2 = ((7 * -8 + x * -8) + x(7 + x)) + -10
60 + 17x + x2 = ((-56 + -8x) + x(7 + x)) + -10
60 + 17x + x2 = (-56 + -8x + (7 * x + x * x)) + -10
60 + 17x + x2 = (-56 + -8x + (7x + x2)) + -10

Combine like terms: -8x + 7x = -1x
60 + 17x + x2 = (-56 + -1x + x2) + -10

Reorder the terms:
60 + 17x + x2 = -56 + -10 + -1x + x2

Combine like terms: -56 + -10 = -66
60 + 17x + x2 = -66 + -1x + x2

Add '-1x2' to each side of the equation.
60 + 17x + x2 + -1x2 = -66 + -1x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
60 + 17x + 0 = -66 + -1x + x2 + -1x2
60 + 17x = -66 + -1x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
60 + 17x = -66 + -1x + 0
60 + 17x = -66 + -1x

Solving
60 + 17x = -66 + -1x

Solving for variable 'x'.

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

Add 'x' to each side of the equation.
60 + 17x + x = -66 + -1x + x

Combine like terms: 17x + x = 18x
60 + 18x = -66 + -1x + x

Combine like terms: -1x + x = 0
60 + 18x = -66 + 0
60 + 18x = -66

Add '-60' to each side of the equation.
60 + -60 + 18x = -66 + -60

Combine like terms: 60 + -60 = 0
0 + 18x = -66 + -60
18x = -66 + -60

Combine like terms: -66 + -60 = -126
18x = -126

Divide each side by '18'.
x = -7

Simplifying
x = -7

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