X-3x(1-12x)=11-(5-6x)(6x+5)

To solve the equation x-3x(1-12x)=11-(5-6x)(6x+5), let's simplify each side step by step:

Starting with the left side of the equation:

x - 3x(1 - 12x) = x - 3x + 36x^2 = -2x + 36x^2

Next, let's simplify the parentheses on the right side of the equation:

11 - (5 - 6x)(6x + 5) = 11 - (5(6x + 5) - 6x(6x + 5)) = 11 - (30x + 25 - 36x^2 - 30x) = 11 - (5 - 30x - 36x^2) = 11 - 5 + 30x + 36x^2 = 6 + 30x + 36x^2

Now let's rewrite the equation with the simplified expressions:

-2x + 36x^2 = 6 + 30x + 36x^2

Since we have a quadratic equation, let's move all the terms to one side to solve for x:

-2x - 30x - 36x^2 + 36x^2 - 6 = 0

Combining like terms:

-32x - 6 = 0

To isolate x, let's move the constant term to the other side:

-32x = 6

Now divide both sides of the equation by -32:

x = 6/-32

Simplifying:

x = -3/16

So the solution to the equation is x = -3/16.