Question 347025
{{{2x^2+7x-5 = x^2+6x+7}}}
This is a quadratic equation. So we want one side e4qual to zero. I'll start by subtracting the entire right side of the equation from both sides:
{{{2x^2+7x-5 - (x^2+6x+7) = x^2+6x+7 - (x^2+6x+7)}}}
giving us:
{{{x^2 + x -12 = 0}}}
Now we factor (or use the Quadratic Formula). This factors pretty easily. The factors of -12 that add up to 1 are 4 and -3:
{{{(x+4)(x-3) = 0}}}
From the Zero Product property we know that this (or any) product can be zero <i>only</i> if one (or more) of the factors is zero. So:
x+4 = 0 or x-3 = 0
Solving these we get:
x = -4 or x = 3
These are the solutions to your equation.