(2r-1)(2x^2+4x+1)=

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Solution for (2r-1)(2x^2+4x+1)= equation: 


Simplifying
(2r + -1)(2x2 + 4x + 1) = 0

Reorder the terms:
(-1 + 2r)(2x2 + 4x + 1) = 0

Reorder the terms:
(-1 + 2r)(1 + 4x + 2x2) = 0

Multiply (-1 + 2r) * (1 + 4x + 2x2)
(-1(1 + 4x + 2x2) + 2r * (1 + 4x + 2x2)) = 0
((1 * -1 + 4x * -1 + 2x2 * -1) + 2r * (1 + 4x + 2x2)) = 0
((-1 + -4x + -2x2) + 2r * (1 + 4x + 2x2)) = 0
(-1 + -4x + -2x2 + (1 * 2r + 4x * 2r + 2x2 * 2r)) = 0
(-1 + -4x + -2x2 + (2r + 8rx + 4rx2)) = 0

Reorder the terms:
(-1 + 2r + 8rx + 4rx2 + -4x + -2x2) = 0
(-1 + 2r + 8rx + 4rx2 + -4x + -2x2) = 0

Solving
-1 + 2r + 8rx + 4rx2 + -4x + -2x2 = 0

Solving for variable 'r'.

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

Add '1' to each side of the equation.
-1 + 2r + 8rx + 4rx2 + -4x + 1 + -2x2 = 0 + 1

Reorder the terms:
-1 + 1 + 2r + 8rx + 4rx2 + -4x + -2x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2r + 8rx + 4rx2 + -4x + -2x2 = 0 + 1
2r + 8rx + 4rx2 + -4x + -2x2 = 0 + 1

Combine like terms: 0 + 1 = 1
2r + 8rx + 4rx2 + -4x + -2x2 = 1

Add '4x' to each side of the equation.
2r + 8rx + 4rx2 + -4x + 4x + -2x2 = 1 + 4x

Combine like terms: -4x + 4x = 0
2r + 8rx + 4rx2 + 0 + -2x2 = 1 + 4x
2r + 8rx + 4rx2 + -2x2 = 1 + 4x

Add '2x2' to each side of the equation.
2r + 8rx + 4rx2 + -2x2 + 2x2 = 1 + 4x + 2x2

Combine like terms: -2x2 + 2x2 = 0
2r + 8rx + 4rx2 + 0 = 1 + 4x + 2x2
2r + 8rx + 4rx2 = 1 + 4x + 2x2

Reorder the terms:
-1 + 2r + 8rx + 4rx2 + -4x + -2x2 = 1 + 4x + 2x2 + -1 + -4x + -2x2

Reorder the terms:
-1 + 2r + 8rx + 4rx2 + -4x + -2x2 = 1 + -1 + 4x + -4x + 2x2 + -2x2

Combine like terms: 1 + -1 = 0
-1 + 2r + 8rx + 4rx2 + -4x + -2x2 = 0 + 4x + -4x + 2x2 + -2x2
-1 + 2r + 8rx + 4rx2 + -4x + -2x2 = 4x + -4x + 2x2 + -2x2

Combine like terms: 4x + -4x = 0
-1 + 2r + 8rx + 4rx2 + -4x + -2x2 = 0 + 2x2 + -2x2
-1 + 2r + 8rx + 4rx2 + -4x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-1 + 2r + 8rx + 4rx2 + -4x + -2x2 = 0

The solution to this equation could not be determined.

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