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

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


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

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

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

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

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

Reorder the terms:
-2 + 1x + 5x + 6x2 = 4 + (3x + 1)(2x + 1)

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

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

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

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

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

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

Add '-6x2' to each side of the equation.
-2 + 6x + 6x2 + -6x2 = 5 + 5x + 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-2 + 6x + 0 = 5 + 5x + 6x2 + -6x2
-2 + 6x = 5 + 5x + 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-2 + 6x = 5 + 5x + 0
-2 + 6x = 5 + 5x

Solving
-2 + 6x = 5 + 5x

Solving for variable 'x'.

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

Add '-5x' to each side of the equation.
-2 + 6x + -5x = 5 + 5x + -5x

Combine like terms: 6x + -5x = 1x
-2 + 1x = 5 + 5x + -5x

Combine like terms: 5x + -5x = 0
-2 + 1x = 5 + 0
-2 + 1x = 5

Add '2' to each side of the equation.
-2 + 2 + 1x = 5 + 2

Combine like terms: -2 + 2 = 0
0 + 1x = 5 + 2
1x = 5 + 2

Combine like terms: 5 + 2 = 7
1x = 7

Divide each side by '1'.
x = 7

Simplifying
x = 7

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