(x-5)(x+1)+(2x-5)(x+2)-(x+7)(3x-4)=2

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Solution for (x-5)(x+1)+(2x-5)(x+2)-(x+7)(3x-4)=2 equation: 


Simplifying
(x + -5)(x + 1) + (2x + -5)(x + 2) + -1(x + 7)(3x + -4) = 2

Reorder the terms:
(-5 + x)(x + 1) + (2x + -5)(x + 2) + -1(x + 7)(3x + -4) = 2

Reorder the terms:
(-5 + x)(1 + x) + (2x + -5)(x + 2) + -1(x + 7)(3x + -4) = 2

Multiply (-5 + x) * (1 + x)
(-5(1 + x) + x(1 + x)) + (2x + -5)(x + 2) + -1(x + 7)(3x + -4) = 2
((1 * -5 + x * -5) + x(1 + x)) + (2x + -5)(x + 2) + -1(x + 7)(3x + -4) = 2
((-5 + -5x) + x(1 + x)) + (2x + -5)(x + 2) + -1(x + 7)(3x + -4) = 2
(-5 + -5x + (1 * x + x * x)) + (2x + -5)(x + 2) + -1(x + 7)(3x + -4) = 2
(-5 + -5x + (1x + x2)) + (2x + -5)(x + 2) + -1(x + 7)(3x + -4) = 2

Combine like terms: -5x + 1x = -4x
(-5 + -4x + x2) + (2x + -5)(x + 2) + -1(x + 7)(3x + -4) = 2

Reorder the terms:
-5 + -4x + x2 + (-5 + 2x)(x + 2) + -1(x + 7)(3x + -4) = 2

Reorder the terms:
-5 + -4x + x2 + (-5 + 2x)(2 + x) + -1(x + 7)(3x + -4) = 2

Multiply (-5 + 2x) * (2 + x)
-5 + -4x + x2 + (-5(2 + x) + 2x * (2 + x)) + -1(x + 7)(3x + -4) = 2
-5 + -4x + x2 + ((2 * -5 + x * -5) + 2x * (2 + x)) + -1(x + 7)(3x + -4) = 2
-5 + -4x + x2 + ((-10 + -5x) + 2x * (2 + x)) + -1(x + 7)(3x + -4) = 2
-5 + -4x + x2 + (-10 + -5x + (2 * 2x + x * 2x)) + -1(x + 7)(3x + -4) = 2
-5 + -4x + x2 + (-10 + -5x + (4x + 2x2)) + -1(x + 7)(3x + -4) = 2

Combine like terms: -5x + 4x = -1x
-5 + -4x + x2 + (-10 + -1x + 2x2) + -1(x + 7)(3x + -4) = 2

Reorder the terms:
-5 + -4x + x2 + -10 + -1x + 2x2 + -1(7 + x)(3x + -4) = 2

Reorder the terms:
-5 + -4x + x2 + -10 + -1x + 2x2 + -1(7 + x)(-4 + 3x) = 2

Multiply (7 + x) * (-4 + 3x)
-5 + -4x + x2 + -10 + -1x + 2x2 + -1(7(-4 + 3x) + x(-4 + 3x)) = 2
-5 + -4x + x2 + -10 + -1x + 2x2 + -1((-4 * 7 + 3x * 7) + x(-4 + 3x)) = 2
-5 + -4x + x2 + -10 + -1x + 2x2 + -1((-28 + 21x) + x(-4 + 3x)) = 2
-5 + -4x + x2 + -10 + -1x + 2x2 + -1(-28 + 21x + (-4 * x + 3x * x)) = 2
-5 + -4x + x2 + -10 + -1x + 2x2 + -1(-28 + 21x + (-4x + 3x2)) = 2

Combine like terms: 21x + -4x = 17x
-5 + -4x + x2 + -10 + -1x + 2x2 + -1(-28 + 17x + 3x2) = 2
-5 + -4x + x2 + -10 + -1x + 2x2 + (-28 * -1 + 17x * -1 + 3x2 * -1) = 2
-5 + -4x + x2 + -10 + -1x + 2x2 + (28 + -17x + -3x2) = 2

Reorder the terms:
-5 + -10 + 28 + -4x + -1x + -17x + x2 + 2x2 + -3x2 = 2

Combine like terms: -5 + -10 = -15
-15 + 28 + -4x + -1x + -17x + x2 + 2x2 + -3x2 = 2

Combine like terms: -15 + 28 = 13
13 + -4x + -1x + -17x + x2 + 2x2 + -3x2 = 2

Combine like terms: -4x + -1x = -5x
13 + -5x + -17x + x2 + 2x2 + -3x2 = 2

Combine like terms: -5x + -17x = -22x
13 + -22x + x2 + 2x2 + -3x2 = 2

Combine like terms: x2 + 2x2 = 3x2
13 + -22x + 3x2 + -3x2 = 2

Combine like terms: 3x2 + -3x2 = 0
13 + -22x + 0 = 2
13 + -22x = 2

Solving
13 + -22x = 2

Solving for variable 'x'.

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

Add '-13' to each side of the equation.
13 + -13 + -22x = 2 + -13

Combine like terms: 13 + -13 = 0
0 + -22x = 2 + -13
-22x = 2 + -13

Combine like terms: 2 + -13 = -11
-22x = -11

Divide each side by '-22'.
x = 0.5

Simplifying
x = 0.5

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