2х^2+14х-80=х(х+14)+20

To solve the equation \(2x^2 + 14x - 80 = x(x + 14) + 20\), we first simplify both sides of the equation.

Starting with the left side:

\(2x^2 + 14x - 80\)

Factor out the right side:

\(2x^2 + 14x - 80 = 2(x^2 + 7x - 40)\)

Now, let's factorize \(x(x + 14) + 20\) on the right side of the equation:

\(x(x + 14) + 20 = x^2 + 14x + 20\)

Now we have the equation:

\(2(x^2 + 7x - 40) = x^2 + 14x + 20\)

Expand the left side:

\(2x^2 + 14x - 80 = x^2 + 14x + 20\)

Now, we have a quadratic equation. To solve it, first, bring all terms to one side to set the equation to zero:

\(2x^2 + 14x - 80 - x^2 - 14x - 20 = 0\)

Simplify:

\(x^2 - 100 = 0\)

Now, solve for \(x\) by factoring:

\((x - 10)(x + 10) = 0\)

Therefore, the solutions to the equation are \(x = 10\) and \(x = -10\).