Questions: Solve by applying the zero product property. 10 m(m+4)=7 m-20 The solution set is

Transcript text: Solve by applying the zero product property. \[ 10 m(m+4)=7 m-20 \] If there is more than one solution, separate the The solution set is $\square$ \}

Solution

Solution Steps

To solve the equation $10m(m+4) = 7m - 20$ using the zero product property, we first need to rearrange the equation to set it to zero. This involves moving all terms to one side of the equation. Once the equation is in the form of a polynomial equal to zero, we can factor it. After factoring, we apply the zero product property, which states that if the product of factors is zero, then at least one of the factors must be zero. We solve each factor set to zero to find the possible solutions for $m$.

Step 1: Rearrange the Equation

To solve the equation $10m(m+4) = 7m - 20$, we first rearrange it to set it to zero: \[ 10m(m+4) - 7m + 20 = 0 \]

Step 2: Expand and Simplify

Expand the left side of the equation: \[ 10m^2 + 40m - 7m + 20 = 0 \] Simplify by combining like terms: \[ 10m^2 + 33m + 20 = 0 \]

Step 3: Factor the Quadratic Equation

The quadratic equation $10m^2 + 33m + 20 = 0$ can be factored into: \[ (2m + 5)(5m + 4) = 0 \]

Step 4: Apply the Zero Product Property

Using the zero product property, set each factor equal to zero and solve for $m$: