What is the answer to ((2x-1)(2x+1))/4 =(3(4x^2+1))/(12)-x ?

The answer to ((2x-1)(2x+1))/4 =(3(4x^2+1))/(12)-x is x= 1/2

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((2x-1)(2x+1))/4 =(3(4x^2+1))/(12)-x

\frac{( 2 x - 1 ) ( 2 x + 1 )}{4} = \frac{3 ( 4 x ^{2} + 1 )}{12} - x

x = \frac{1}{2}

Solution steps

\frac{( 2 x - 1 ) ( 2 x + 1 )}{4} = \frac{3 ( 4 x ^{2} + 1 )}{12} - x

Cancel

\frac{3 ( 4 x ^{2} + 1 )}{12} : \frac{4 x ^{2} + 1}{4}

\frac{( 2 x - 1 ) ( 2 x + 1 )}{4} = \frac{4 x ^{2} + 1}{4} - x

Multiply both sides by

4

(2 x - 1) (2 x + 1) = 4 x^{2} + 1 - 4 x

Expand

(2 x - 1) (2 x + 1) : 4 x^{2} - 1

4 x^{2} - 1 = 4 x^{2} + 1 - 4 x

Move

1

to the right side

4 x^{2} = 4 x^{2} - 4 x + 2

Subtract

4 x^{2} - 4 x

from both sides

4 x^{2} - (4 x^{2} - 4 x) = 4 x^{2} - 4 x + 2 - (4 x^{2} - 4 x)

Simplify

4 x = 2

Divide both sides by

4

x = \frac{1}{2}

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

b^{4} - 256

1 0^{0.4}

5 (x + 4) > 5 x + 10

x^{5} \geq x^{3}

What is the answer to ((2x-1)(2x+1))/4 =(3(4x^2+1))/(12)-x ?
The answer to ((2x-1)(2x+1))/4 =(3(4x^2+1))/(12)-x is x= 1/2
Solve for x: ((2x-1)(2x+1))/4 =(3(4x^2+1))/(12)-x
The solution is x= 1/2