What are the solutions to the equation (2x-1)(x^2+2x+1)=2x^2+2x ?

The solutions to the equation (2x-1)(x^2+2x+1)=2x^2+2x are x=-1/2 ,x=-1,x=1

Find the zeros of (2x-1)(x^2+2x+1)=2x^2+2x

The zeros of (2x-1)(x^2+2x+1)=2x^2+2x are x=-1/2 ,x=-1,x=1

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

x = - \frac{1}{2}, x = - 1, x = 1

Decimal

x = - 0.5, x = - 1, x = 1

Solution steps

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

Expand

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

2 x^{3} + 3 x^{2} - 1 = 2 x^{2} + 2 x

Move

2 x

to the left side

2 x^{3} + 3 x^{2} - 1 - 2 x = 2 x^{2}

Move

2 x^{2}

to the left side

2 x^{3} + x^{2} - 2 x - 1 = 0

Factor

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

(2 x + 1) (x + 1) (x - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

2 x + 1 = 0 or x + 1 = 0 or x - 1 = 0

Solve

2 x + 1 = 0 : x = - \frac{1}{2}

Solve

x + 1 = 0 : x = - 1

Solve

x - 1 = 0 : x = 1

The solutions are

x = - \frac{1}{2}, x = - 1, x = 1

x^{3} + 1

x^{7} - x^{4} - x^{3} + 1 = 0

4 x^{3} + 24 x^{2} = 0

x^{3} + 3 x^{2} + 3 x + 1

x^{3} - 75 x - 250 = 0

What are the solutions to the equation (2x-1)(x^2+2x+1)=2x^2+2x ?
The solutions to the equation (2x-1)(x^2+2x+1)=2x^2+2x are x=-1/2 ,x=-1,x=1
Find the zeros of (2x-1)(x^2+2x+1)=2x^2+2x
The zeros of (2x-1)(x^2+2x+1)=2x^2+2x are x=-1/2 ,x=-1,x=1