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

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


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

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

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

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

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

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

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

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

Combine like terms: 10x + -2x = 8x
-1 + 1x + 2x2 = (-5 + 8x + 4x2)

Solving
-1 + 1x + 2x2 = -5 + 8x + 4x2

Solving for variable 'x'.

Reorder the terms:
-1 + 5 + 1x + -8x + 2x2 + -4x2 = -5 + 8x + 4x2 + 5 + -8x + -4x2

Combine like terms: -1 + 5 = 4
4 + 1x + -8x + 2x2 + -4x2 = -5 + 8x + 4x2 + 5 + -8x + -4x2

Combine like terms: 1x + -8x = -7x
4 + -7x + 2x2 + -4x2 = -5 + 8x + 4x2 + 5 + -8x + -4x2

Combine like terms: 2x2 + -4x2 = -2x2
4 + -7x + -2x2 = -5 + 8x + 4x2 + 5 + -8x + -4x2

Reorder the terms:
4 + -7x + -2x2 = -5 + 5 + 8x + -8x + 4x2 + -4x2

Combine like terms: -5 + 5 = 0
4 + -7x + -2x2 = 0 + 8x + -8x + 4x2 + -4x2
4 + -7x + -2x2 = 8x + -8x + 4x2 + -4x2

Combine like terms: 8x + -8x = 0
4 + -7x + -2x2 = 0 + 4x2 + -4x2
4 + -7x + -2x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
4 + -7x + -2x2 = 0

Factor a trinomial.
(1 + -2x)(4 + x) = 0


Subproblem 1
Set the factor '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2x = 0 + -1

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

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

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5

Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Solution
x = {0.5, -4}

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