(x+2)(2x+1)=(2x+3)(x+6)

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Solution for (x+2)(2x+1)=(2x+3)(x+6) equation: 


Simplifying
(x + 2)(2x + 1) = (2x + 3)(x + 6)

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

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

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

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

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

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

Multiply (3 + 2x) * (6 + x)
2 + 5x + 2x2 = (3(6 + x) + 2x * (6 + x))
2 + 5x + 2x2 = ((6 * 3 + x * 3) + 2x * (6 + x))
2 + 5x + 2x2 = ((18 + 3x) + 2x * (6 + x))
2 + 5x + 2x2 = (18 + 3x + (6 * 2x + x * 2x))
2 + 5x + 2x2 = (18 + 3x + (12x + 2x2))

Combine like terms: 3x + 12x = 15x
2 + 5x + 2x2 = (18 + 15x + 2x2)

Add '-2x2' to each side of the equation.
2 + 5x + 2x2 + -2x2 = 18 + 15x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
2 + 5x + 0 = 18 + 15x + 2x2 + -2x2
2 + 5x = 18 + 15x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
2 + 5x = 18 + 15x + 0
2 + 5x = 18 + 15x

Solving
2 + 5x = 18 + 15x

Solving for variable 'x'.

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

Add '-15x' to each side of the equation.
2 + 5x + -15x = 18 + 15x + -15x

Combine like terms: 5x + -15x = -10x
2 + -10x = 18 + 15x + -15x

Combine like terms: 15x + -15x = 0
2 + -10x = 18 + 0
2 + -10x = 18

Add '-2' to each side of the equation.
2 + -2 + -10x = 18 + -2

Combine like terms: 2 + -2 = 0
0 + -10x = 18 + -2
-10x = 18 + -2

Combine like terms: 18 + -2 = 16
-10x = 16

Divide each side by '-10'.
x = -1.6

Simplifying
x = -1.6

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