Question

Solve the equation. $$ 5(3 m+9)(5 m-15)=0 $$

Short answer

The solutions to the equation \(5(3m+9)(5m-15) = 0\) are \(m = -3\) and \(m = 3\).

Step-by-step solution

Simplify Equation

The given equation is\(5(3m+9)(5m-15)=0\). First note that the equation is set equal to zero. This allows to split the equation into two parts, setting each part of the equation equal to zero.

Solve for m in the First Equation

From the first part of the equation \((3m+9)\), set it equal to zero and solve for \(m\). Thus the equation becomes \(3m+9 = 0\). Subtract 9 from both sides to get \(3m = -9\). Finally, divide both sides by 3 to get \(m = -9 / 3 = -3\). This is the first possible solution for m.

Solve for m in the Second Equation

Next, from the second part of the equation \((5m-15)\), set it equal to zero and solve for \(m\). The equation becomes \(5m - 15 = 0\). Add 15 to both sides to get \(5m = 15\). Finally, divide both sides by 5 to get \(m = 15 / 5 = 3\). This is the second possible solution for m.