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

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


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

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

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

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

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

Combine like terms: x + 7x = 8x
4 + 8x + 3x2 = (2x + 3)(2x + -1) + -1x(x + -2)

Reorder the terms:
4 + 8x + 3x2 = (3 + 2x)(2x + -1) + -1x(x + -2)

Reorder the terms:
4 + 8x + 3x2 = (3 + 2x)(-1 + 2x) + -1x(x + -2)

Multiply (3 + 2x) * (-1 + 2x)
4 + 8x + 3x2 = (3(-1 + 2x) + 2x * (-1 + 2x)) + -1x(x + -2)
4 + 8x + 3x2 = ((-1 * 3 + 2x * 3) + 2x * (-1 + 2x)) + -1x(x + -2)
4 + 8x + 3x2 = ((-3 + 6x) + 2x * (-1 + 2x)) + -1x(x + -2)
4 + 8x + 3x2 = (-3 + 6x + (-1 * 2x + 2x * 2x)) + -1x(x + -2)
4 + 8x + 3x2 = (-3 + 6x + (-2x + 4x2)) + -1x(x + -2)

Combine like terms: 6x + -2x = 4x
4 + 8x + 3x2 = (-3 + 4x + 4x2) + -1x(x + -2)

Reorder the terms:
4 + 8x + 3x2 = -3 + 4x + 4x2 + -1x(-2 + x)
4 + 8x + 3x2 = -3 + 4x + 4x2 + (-2 * -1x + x * -1x)
4 + 8x + 3x2 = -3 + 4x + 4x2 + (2x + -1x2)

Reorder the terms:
4 + 8x + 3x2 = -3 + 4x + 2x + 4x2 + -1x2

Combine like terms: 4x + 2x = 6x
4 + 8x + 3x2 = -3 + 6x + 4x2 + -1x2

Combine like terms: 4x2 + -1x2 = 3x2
4 + 8x + 3x2 = -3 + 6x + 3x2

Add '-3x2' to each side of the equation.
4 + 8x + 3x2 + -3x2 = -3 + 6x + 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
4 + 8x + 0 = -3 + 6x + 3x2 + -3x2
4 + 8x = -3 + 6x + 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
4 + 8x = -3 + 6x + 0
4 + 8x = -3 + 6x

Solving
4 + 8x = -3 + 6x

Solving for variable 'x'.

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

Add '-6x' to each side of the equation.
4 + 8x + -6x = -3 + 6x + -6x

Combine like terms: 8x + -6x = 2x
4 + 2x = -3 + 6x + -6x

Combine like terms: 6x + -6x = 0
4 + 2x = -3 + 0
4 + 2x = -3

Add '-4' to each side of the equation.
4 + -4 + 2x = -3 + -4

Combine like terms: 4 + -4 = 0
0 + 2x = -3 + -4
2x = -3 + -4

Combine like terms: -3 + -4 = -7
2x = -7

Divide each side by '2'.
x = -3.5

Simplifying
x = -3.5

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