4x(x-6)-5x(x-5)=-2

Solve for X

To solve the equation 4x(x-6)-5x(x-5)=-2, we will follow these steps:

Step 1: Simplify both sides of the equation by distributing.
4x(x-6) - 5x(x-5) = -2
4x^2 - 24x - 5x^2 + 25x = -2

Step 2: Combine like terms on the left side of the equation.
(4x^2 - 5x^2) + (-24x + 25x) = -2
-x^2 + x = -2

Step 3: Move all terms to one side of the equation to form a quadratic equation.
x^2 - x - 2 = 0

Now we have a quadratic equation in the form ax^2 + bx + c = 0, where a = 1, b = -1, and c = -2.

Step 4: Solve the quadratic equation by factoring, completing the square, or using the quadratic formula.

In this case, let's solve it by factoring.
(x - 2)(x + 1) = 0

Step 5: Set each factor equal to zero and solve for x.
x - 2 = 0
x = 2

x + 1 = 0
x = -1

Therefore, the solutions to the equation 4x(x-6)-5x(x-5)=-2 are x = 2 and x = -1.