Step-by-step explanation: To solve the equation 2x(2x-5)=36, we first need to distribute the 2x:
2x(2x-5) = 2x * 2x - 2x * 5 = 4x^2 - 10x
Now that we have the expanded equation, we can set it equal to 36:
4x^2 - 10x = 36
Next, we'll isolate x by subtracting 36 from both sides:
4x^2 - 10x - 36 = 0
This is a quadratic equation, which we can solve using the quadratic formula or by factoring. Here's one way to solve it using factoring:
(2x-9)(2x+4) = 0
We can set each factor equal to zero and solve for x:
2x-9 = 0, so x = 9/2
2x+4 = 0, so x = -4/2 = -2
So x = 9/2 and x = -2 are the solutions to the equation 2x(2x-5)=36.