Question

(5y+2)(14y-5)=(7y+1)(10y+4)

Answer 1

      2                                  2
70у  -  25у + 28у - 10=70у   +  28у + 10у + 4


-25у - 10=10у+4


-25у-10у=4+10


-35у=14


        2
у= -  -
        5

Answer 2

To solve the given equation, you need to expand both sides and then simplify to find the value of 'y'. Let's go step by step:

Step 1: Expand both sides of the equation

On the left-hand side: (5y + 2)(14y - 5) = 5y * 14y + 5y * (-5) + 2 * 14y + 2 * (-5) = 70y^2 - 25y + 28y - 10

On the right-hand side: (7y + 1)(10y + 4) = 7y * 10y + 7y * 4 + 1 * 10y + 1 * 4 = 70y^2 + 28y + 10y + 4

Step 2: Combine like terms

Now, the equation becomes: 70y^2 - 25y + 28y - 10 = 70y^2 + 28y + 10y + 4

Step 3: Move all the terms to one side of the equation

To do this, we will subtract the right-hand side from the left-hand side: 70y^2 - 25y + 28y - 10 - (70y^2 + 28y + 10y + 4) = 0

Step 4: Simplify the equation further

Combine like terms again: 70y^2 - 25y + 28y - 10 - 70y^2 - 38y - 4 = 0

Step 5: Continue simplification

Now, simplify further: (70y^2 - 70y^2) + (28y - 25y - 38y) - (10 + 4) = 0

Simplify inside the parentheses: 0 - 35y - 14 = 0

Step 6: Final step - solve for 'y'

Now, isolate 'y' on one side: -35y - 14 = 0

Add 14 to both sides: -35y = 14

Finally, divide both sides by -35 to solve for 'y': y = 14 / -35 y = -2/5

So, the value of 'y' that satisfies the given equation is y = -2/5.