(x+2)(2x+3)+5=(2x+1)(x+4)-16

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Solution for (x+2)(2x+3)+5=(2x+1)(x+4)-16 equation: 


Simplifying
(x + 2)(2x + 3) + 5 = (2x + 1)(x + 4) + -16

Reorder the terms:
(2 + x)(2x + 3) + 5 = (2x + 1)(x + 4) + -16

Reorder the terms:
(2 + x)(3 + 2x) + 5 = (2x + 1)(x + 4) + -16

Multiply (2 + x) * (3 + 2x)
(2(3 + 2x) + x(3 + 2x)) + 5 = (2x + 1)(x + 4) + -16
((3 * 2 + 2x * 2) + x(3 + 2x)) + 5 = (2x + 1)(x + 4) + -16
((6 + 4x) + x(3 + 2x)) + 5 = (2x + 1)(x + 4) + -16
(6 + 4x + (3 * x + 2x * x)) + 5 = (2x + 1)(x + 4) + -16
(6 + 4x + (3x + 2x2)) + 5 = (2x + 1)(x + 4) + -16

Combine like terms: 4x + 3x = 7x
(6 + 7x + 2x2) + 5 = (2x + 1)(x + 4) + -16

Reorder the terms:
6 + 5 + 7x + 2x2 = (2x + 1)(x + 4) + -16

Combine like terms: 6 + 5 = 11
11 + 7x + 2x2 = (2x + 1)(x + 4) + -16

Reorder the terms:
11 + 7x + 2x2 = (1 + 2x)(x + 4) + -16

Reorder the terms:
11 + 7x + 2x2 = (1 + 2x)(4 + x) + -16

Multiply (1 + 2x) * (4 + x)
11 + 7x + 2x2 = (1(4 + x) + 2x * (4 + x)) + -16
11 + 7x + 2x2 = ((4 * 1 + x * 1) + 2x * (4 + x)) + -16
11 + 7x + 2x2 = ((4 + 1x) + 2x * (4 + x)) + -16
11 + 7x + 2x2 = (4 + 1x + (4 * 2x + x * 2x)) + -16
11 + 7x + 2x2 = (4 + 1x + (8x + 2x2)) + -16

Combine like terms: 1x + 8x = 9x
11 + 7x + 2x2 = (4 + 9x + 2x2) + -16

Reorder the terms:
11 + 7x + 2x2 = 4 + -16 + 9x + 2x2

Combine like terms: 4 + -16 = -12
11 + 7x + 2x2 = -12 + 9x + 2x2

Add '-2x2' to each side of the equation.
11 + 7x + 2x2 + -2x2 = -12 + 9x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
11 + 7x + 0 = -12 + 9x + 2x2 + -2x2
11 + 7x = -12 + 9x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
11 + 7x = -12 + 9x + 0
11 + 7x = -12 + 9x

Solving
11 + 7x = -12 + 9x

Solving for variable 'x'.

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

Add '-9x' to each side of the equation.
11 + 7x + -9x = -12 + 9x + -9x

Combine like terms: 7x + -9x = -2x
11 + -2x = -12 + 9x + -9x

Combine like terms: 9x + -9x = 0
11 + -2x = -12 + 0
11 + -2x = -12

Add '-11' to each side of the equation.
11 + -11 + -2x = -12 + -11

Combine like terms: 11 + -11 = 0
0 + -2x = -12 + -11
-2x = -12 + -11

Combine like terms: -12 + -11 = -23
-2x = -23

Divide each side by '-2'.
x = 11.5

Simplifying
x = 11.5

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