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

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


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

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

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

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

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

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

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

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

Combine like terms: 12x + 3x = 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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