Question 167899
Congratulation for trying, Rachel!
Solve for x:
{{{4x*(x-2)-5x*(x-1) = 2}}} First, apply the distributive to both sets of parentheses.
{{{(4x^2-8x)-(5x^2-5x) = 2}}} Now combine like-terms.
{{{(4x^2-5x^2)-(8x-5x) = 2}}}
{{{-x^2-3x = 2}}} Subtract 2 from both sides of the equation.
{{{-x^2-3x-2 = 0}}} Multiply through by -1 to make the terms positive and a little easier to work with. This will not change the result any.
{{{x^2+3x+2 = 0}}} Now factor the trinomial.
{{{(x+1)(x+2) = 0}}} Apply the zero product rule: If A*B = 0, then either A = 0 or B = 0 or both, so...
{{{(x+1) = 0}}} or {{{(x+2) = 0}}} which means that...
{{{x = -1}}} or {{{x = -2}}}
You can verify the solution by substituting the values into original equation.