Solve the equation by factoring, show all work.
4x^2-7x=x
4x^2-7x = x.
4x^2-7x-x = 0,
4x^2-8x = 0,
Factor out 4x and finish the problem.
To solve the equation 4x^2 - 7x = x by factoring, we need to rearrange the equation so that one side is equal to zero.
The equation can be rewritten as:
4x^2 - x - 7x = 0
Combine like terms:
4x^2 - 8x = 0
Now, we can factor out the greatest common factor, which in this case is 4x:
4x(x - 2) = 0
Now, we have a product of two factors equal to zero. To find the solutions, we can set each factor equal to zero and solve for x:
4x = 0 or x - 2 = 0
For the first factor:
4x = 0
Divide both sides by 4:
x = 0
For the second factor:
x - 2 = 0
Add 2 to both sides:
x = 2
Therefore, the solutions to the equation 4x^2 - 7x = x are x = 0 and x = 2.