Question

Solve the equation if possible. $$ -2(6-10 n)=10(2 n-6) $$

Short answer

The equation has no solution.

Step-by-step solution

Distribute the constants

Distribute \(-2\) into the parentheses on the left side to get \(-2*6 + (-2)*(-10n) = -12+20n\). Similarly, distribute \(10\) into the parentheses on the right side to get \(10*2n - 10*6 = 20n-60\). The equation becomes \(-12+20n = 20n-60\).

Combine like terms

Combine like terms by subtracting \(20n\) from both sides of the equation. This gives \(-12 = -60\).

Evaluate the equality

The equation \(-12 = -60\) is clearly false. This disregard implies there's no \( n \) that will satisfy the original equation.