(2x+1)(x+1)=(x-2)(2x+5)

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


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

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

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

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

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

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

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

Multiply (-2 + x) * (5 + 2x)
1 + 3x + 2x2 = (-2(5 + 2x) + x(5 + 2x))
1 + 3x + 2x2 = ((5 * -2 + 2x * -2) + x(5 + 2x))
1 + 3x + 2x2 = ((-10 + -4x) + x(5 + 2x))
1 + 3x + 2x2 = (-10 + -4x + (5 * x + 2x * x))
1 + 3x + 2x2 = (-10 + -4x + (5x + 2x2))

Combine like terms: -4x + 5x = 1x
1 + 3x + 2x2 = (-10 + 1x + 2x2)

Add '-2x2' to each side of the equation.
1 + 3x + 2x2 + -2x2 = -10 + 1x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
1 + 3x + 0 = -10 + 1x + 2x2 + -2x2
1 + 3x = -10 + 1x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
1 + 3x = -10 + 1x + 0
1 + 3x = -10 + 1x

Solving
1 + 3x = -10 + 1x

Solving for variable 'x'.

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

Add '-1x' to each side of the equation.
1 + 3x + -1x = -10 + 1x + -1x

Combine like terms: 3x + -1x = 2x
1 + 2x = -10 + 1x + -1x

Combine like terms: 1x + -1x = 0
1 + 2x = -10 + 0
1 + 2x = -10

Add '-1' to each side of the equation.
1 + -1 + 2x = -10 + -1

Combine like terms: 1 + -1 = 0
0 + 2x = -10 + -1
2x = -10 + -1

Combine like terms: -10 + -1 = -11
2x = -11

Divide each side by '2'.
x = -5.5

Simplifying
x = -5.5

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