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

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


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

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

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

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

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

Reorder the terms:
4 + 6x + 2x2 = (1 + 3q)(2x + -1)

Reorder the terms:
4 + 6x + 2x2 = (1 + 3q)(-1 + 2x)

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

Reorder the terms:
4 + 6x + 2x2 = (-1 + -3q + 6qx + 2x)
4 + 6x + 2x2 = (-1 + -3q + 6qx + 2x)

Solving
4 + 6x + 2x2 = -1 + -3q + 6qx + 2x

Solving for variable 'x'.

Reorder the terms:
4 + 1 + 3q + -6qx + 6x + -2x + 2x2 = -1 + -3q + 6qx + 2x + 1 + 3q + -6qx + -2x

Combine like terms: 4 + 1 = 5
5 + 3q + -6qx + 6x + -2x + 2x2 = -1 + -3q + 6qx + 2x + 1 + 3q + -6qx + -2x

Combine like terms: 6x + -2x = 4x
5 + 3q + -6qx + 4x + 2x2 = -1 + -3q + 6qx + 2x + 1 + 3q + -6qx + -2x

Reorder the terms:
5 + 3q + -6qx + 4x + 2x2 = -1 + 1 + -3q + 3q + 6qx + -6qx + 2x + -2x

Combine like terms: -1 + 1 = 0
5 + 3q + -6qx + 4x + 2x2 = 0 + -3q + 3q + 6qx + -6qx + 2x + -2x
5 + 3q + -6qx + 4x + 2x2 = -3q + 3q + 6qx + -6qx + 2x + -2x

Combine like terms: -3q + 3q = 0
5 + 3q + -6qx + 4x + 2x2 = 0 + 6qx + -6qx + 2x + -2x
5 + 3q + -6qx + 4x + 2x2 = 6qx + -6qx + 2x + -2x

Combine like terms: 6qx + -6qx = 0
5 + 3q + -6qx + 4x + 2x2 = 0 + 2x + -2x
5 + 3q + -6qx + 4x + 2x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
5 + 3q + -6qx + 4x + 2x2 = 0

The solution to this equation could not be determined.

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