title: Finding Y given X on a Cubic Bezier Curve?
body: <p>I need a method that allows me to find the Y-coordinate on a Cubic Bezier Curve, given an x-coordinate.</p>
  
  <p>I've come across lots of places telling me to treat it as a cubic function then attempt to find the roots, which I understand. HOWEVER the equation for a Cubic Bezier curve is (for x-coords):</p>
  
  <p><code>X(t) = (1-t)^3 * X0 + 3*(1-t)^2 * t * X1 + 3*(1-t) * t^2 * X2 + t^3 * X3</code></p>
  
  <p>What confuses me is the addition of the <code>(1-t)</code> values. For instance, if I fill in the X values with some random numbers:</p>
  
  <p><code>400 = (1-t)^3 * 100 + 3*(1-t)^2 * t * 600 + 3*(1-t) * t^2 * 800 + t^3 * 800</code></p>
  
  <p>then rearrange it:</p>
  
  <p><code>800t^3 + 3*(1-t)*800t^2 + 3*(1-t)^2*600t +  (1-t)^3*100 -400 = 0</code></p>
  
  <p>I still don't know the value of the <code>(1-t)</code> coefficients. How I am I supposed to solve the equation when <code>(1-t)</code> is still unknown?</p>