5y(y+7)=7(y+7)

If you divide both sides by y+7, you get:

5y = 7

Then divide both sides by 5.

by distributive property:

5y^2+35=7y+49 (addition prop...)
5y^2-7y=49-35
-2y^2=14 (mult. Prop)
y=-2 (answer)

Sorry i 4got 2 multiply y to seven... the correct anser is 7/5...

also y = -7 is a solution

To solve the equation 5y(y+7)=7(y+7), we need to simplify the equation and then calculate the value of y.

Step 1: Distribute the terms on both sides of the equation to remove the parentheses.

5y^2 + 35y = 7y + 49

Step 2: Move all the terms to one side of the equation. Subtract 7y from both sides of the equation.

5y^2 + 35y - 7y = 49

Simplifying this further, we get:

5y^2 + 28y = 49

Step 3: Now, we have a quadratic equation in standard form, 5y^2 + 28y - 49 = 0. To solve this, we can either factor or use the quadratic formula. Let's try factoring first.

The quadratic equation can be factored as:

(5y - 7)(y + 7) = 0

Using the zero product property, we can set each factor equal to zero and solve for y:

5y - 7 = 0 or y + 7 = 0

Solving these two equations, we get:

5y = 7 or y = -7

Dividing both sides of the first equation by 5, we find:

y = 7/5

So, the solutions to the equation 5y(y+7)=7(y+7) are y = 7/5 and y = -7.