What are the solutions to the equation (x-2)(3x+5)=x(x-2) ?

The solutions to the equation (x-2)(3x+5)=x(x-2) are x=2,x=-5/2

Find the zeros of (x-2)(3x+5)=x(x-2)

The zeros of (x-2)(3x+5)=x(x-2) are x=2,x=-5/2

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

x = 2, x = - \frac{5}{2}

Solution steps

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

Move

x (x - 2)

to the left side

(x - 2) (3 x + 5) - x (x - 2) = 0

Factor

(x - 2) (3 x + 5) - x (x - 2) : (x - 2) (2 x + 5)

(x - 2) (2 x + 5) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 2 = 0 or 2 x + 5 = 0

Solve

x - 2 = 0 : x = 2

Solve

2 x + 5 = 0 : x = - \frac{5}{2}

The solutions to the quadratic equation are:

x = 2, x = - \frac{5}{2}

3 x^{2} - 183 = 9

(y + 6) (y - 2) = - 7

- 2 x - 48 = - x^{2}

3 x^{2} + 10 = - 6 x

x^{2} + 2 + x^{2} + 8 x = 3 x^{2} + 4 x - 10

What are the solutions to the equation (x-2)(3x+5)=x(x-2) ?
The solutions to the equation (x-2)(3x+5)=x(x-2) are x=2,x=-5/2
Find the zeros of (x-2)(3x+5)=x(x-2)
The zeros of (x-2)(3x+5)=x(x-2) are x=2,x=-5/2