What are the solutions to the equation x(x-1)=x(7-x) ?

The solutions to the equation x(x-1)=x(7-x) are x=0,x=4

Find the zeros of x(x-1)=x(7-x)

The zeros of x(x-1)=x(7-x) are x=0,x=4

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x (x - 1) = x (7 - x)

x = 0, x = 4

Solution steps

x (x - 1) = x (7 - x)

Move

x (7 - x)

to the left side

x (x - 1) - x (7 - x) = 0

Factor

x (x - 1) - x (7 - x) : 2 x (x - 4)

2 x (x - 4) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x - 4 = 0

Solve

x - 4 = 0 : x = 4

The solutions to the quadratic equation are:

x = 0, x = 4

3 x^{2} + 30 x + 150 = 0

3 x^{2} + a x + 12 = 0

5 x^{2} - 10 x + 9 = 0

2 x^{2} - 4 x = 4

6 x^{2} = - 24 x

What are the solutions to the equation x(x-1)=x(7-x) ?
The solutions to the equation x(x-1)=x(7-x) are x=0,x=4
Find the zeros of x(x-1)=x(7-x)
The zeros of x(x-1)=x(7-x) are x=0,x=4