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

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


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

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

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

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

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

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

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

Multiply (5 + 2x) * (3 + x)
-3 + 2x + x2 + (5(3 + x) + 2x * (3 + x)) + -1(x + 1)(3x + 4) = -2x
-3 + 2x + x2 + ((3 * 5 + x * 5) + 2x * (3 + x)) + -1(x + 1)(3x + 4) = -2x
-3 + 2x + x2 + ((15 + 5x) + 2x * (3 + x)) + -1(x + 1)(3x + 4) = -2x
-3 + 2x + x2 + (15 + 5x + (3 * 2x + x * 2x)) + -1(x + 1)(3x + 4) = -2x
-3 + 2x + x2 + (15 + 5x + (6x + 2x2)) + -1(x + 1)(3x + 4) = -2x

Combine like terms: 5x + 6x = 11x
-3 + 2x + x2 + (15 + 11x + 2x2) + -1(x + 1)(3x + 4) = -2x

Reorder the terms:
-3 + 2x + x2 + 15 + 11x + 2x2 + -1(1 + x)(3x + 4) = -2x

Reorder the terms:
-3 + 2x + x2 + 15 + 11x + 2x2 + -1(1 + x)(4 + 3x) = -2x

Multiply (1 + x) * (4 + 3x)
-3 + 2x + x2 + 15 + 11x + 2x2 + -1(1(4 + 3x) + x(4 + 3x)) = -2x
-3 + 2x + x2 + 15 + 11x + 2x2 + -1((4 * 1 + 3x * 1) + x(4 + 3x)) = -2x
-3 + 2x + x2 + 15 + 11x + 2x2 + -1((4 + 3x) + x(4 + 3x)) = -2x
-3 + 2x + x2 + 15 + 11x + 2x2 + -1(4 + 3x + (4 * x + 3x * x)) = -2x
-3 + 2x + x2 + 15 + 11x + 2x2 + -1(4 + 3x + (4x + 3x2)) = -2x

Combine like terms: 3x + 4x = 7x
-3 + 2x + x2 + 15 + 11x + 2x2 + -1(4 + 7x + 3x2) = -2x
-3 + 2x + x2 + 15 + 11x + 2x2 + (4 * -1 + 7x * -1 + 3x2 * -1) = -2x
-3 + 2x + x2 + 15 + 11x + 2x2 + (-4 + -7x + -3x2) = -2x

Reorder the terms:
-3 + 15 + -4 + 2x + 11x + -7x + x2 + 2x2 + -3x2 = -2x

Combine like terms: -3 + 15 = 12
12 + -4 + 2x + 11x + -7x + x2 + 2x2 + -3x2 = -2x

Combine like terms: 12 + -4 = 8
8 + 2x + 11x + -7x + x2 + 2x2 + -3x2 = -2x

Combine like terms: 2x + 11x = 13x
8 + 13x + -7x + x2 + 2x2 + -3x2 = -2x

Combine like terms: 13x + -7x = 6x
8 + 6x + x2 + 2x2 + -3x2 = -2x

Combine like terms: x2 + 2x2 = 3x2
8 + 6x + 3x2 + -3x2 = -2x

Combine like terms: 3x2 + -3x2 = 0
8 + 6x + 0 = -2x
8 + 6x = -2x

Solving
8 + 6x = -2x

Solving for variable 'x'.

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

Add '2x' to each side of the equation.
8 + 6x + 2x = -2x + 2x

Combine like terms: 6x + 2x = 8x
8 + 8x = -2x + 2x

Combine like terms: -2x + 2x = 0
8 + 8x = 0

Add '-8' to each side of the equation.
8 + -8 + 8x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 8x = 0 + -8
8x = 0 + -8

Combine like terms: 0 + -8 = -8
8x = -8

Divide each side by '8'.
x = -1

Simplifying
x = -1

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