What are the solutions to the equation (2x+3)^2=3x(x+2) ?

The solutions to the equation (2x+3)^2=3x(x+2) are x=-3

Find the zeros of (2x+3)^2=3x(x+2)

The zeros of (2x+3)^2=3x(x+2) are x=-3

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(2 x + 3)^{2} = 3 x (x + 2)

x = - 3

Solution steps

(2 x + 3)^{2} = 3 x (x + 2)

Expand

(2 x + 3)^{2} : 4 x^{2} + 12 x + 9

Expand

3 x (x + 2) : 3 x^{2} + 6 x

4 x^{2} + 12 x + 9 = 3 x^{2} + 6 x

Move

6 x

to the left side

4 x^{2} + 6 x + 9 = 3 x^{2}

Move

3 x^{2}

to the left side

x^{2} + 6 x + 9 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 6 \pm 6 ^{2} - 4 \cdot 1 \cdot 9}{2 \cdot 1}

6^{2} - 4 \cdot 1 \cdot 9 = 0

x_{1, 2} = \frac{- 6 \pm 0}{2 \cdot 1}

x = \frac{- 6}{2 \cdot 1}

\frac{- 6}{2 \cdot 1} = - 3

x = - 3

The solution to the quadratic equation is:

x = - 3

22 c^{2} - 35 c + 12 = - 3 c^{2}

x^{2} - 12 = 0

16 x^{2} - 40 x + 27 = 0

\frac{3}{2} x^{2} - 37.5 = 0

x^{2} = 100

What are the solutions to the equation (2x+3)^2=3x(x+2) ?
The solutions to the equation (2x+3)^2=3x(x+2) are x=-3
Find the zeros of (2x+3)^2=3x(x+2)
The zeros of (2x+3)^2=3x(x+2) are x=-3