What is the answer to (2x+1)^2-(3x-2)^2=5x(2-x) ?

The answer to (2x+1)^2-(3x-2)^2=5x(2-x) is x= 1/2

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(2x+1)^2-(3x-2)^2=5x(2-x)

(2 x + 1)^{2} - (3 x - 2)^{2} = 5 x (2 - x)

x = \frac{1}{2}

Decimal Notation

x = 0.5

Solution steps

(2 x + 1)^{2} - (3 x - 2)^{2} = 5 x (2 - x)

Expand

(2 x + 1)^{2} - (3 x - 2)^{2} : - 5 x^{2} + 16 x - 3

Expand

5 x (2 - x) : 10 x - 5 x^{2}

- 5 x^{2} + 16 x - 3 = 10 x - 5 x^{2}

Move

3

to the right side

- 5 x^{2} + 16 x = 10 x - 5 x^{2} + 3

Subtract

10 x - 5 x^{2}

from both sides

- 5 x^{2} + 16 x - (10 x - 5 x^{2}) = 10 x - 5 x^{2} + 3 - (10 x - 5 x^{2})

Simplify

6 x = 3

Divide both sides by

6

x = \frac{1}{2}

4 x - 29 = 3 x - 2

\frac{2}{3} x y^{2} + 2 x - \frac{1}{3} x y^{2} + \frac{2}{3} x^{2} y - 5 x

x^{5} + x^{4} y^{4}

What is the answer to (2x+1)^2-(3x-2)^2=5x(2-x) ?
The answer to (2x+1)^2-(3x-2)^2=5x(2-x) is x= 1/2
Solve for x: (2x+1)^2-(3x-2)^2=5x(2-x)
The solution is x= 1/2