(3y+2a)(5a-7y)=

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Solution for (3y+2a)(5a-7y)= equation: 


Simplifying
(3y + 2a)(5a + -7y) = 0

Reorder the terms:
(2a + 3y)(5a + -7y) = 0

Multiply (2a + 3y) * (5a + -7y)
(2a * (5a + -7y) + 3y * (5a + -7y)) = 0
((5a * 2a + -7y * 2a) + 3y * (5a + -7y)) = 0

Reorder the terms:
((-14ay + 10a2) + 3y * (5a + -7y)) = 0
((-14ay + 10a2) + 3y * (5a + -7y)) = 0
(-14ay + 10a2 + (5a * 3y + -7y * 3y)) = 0
(-14ay + 10a2 + (15ay + -21y2)) = 0

Reorder the terms:
(-14ay + 15ay + 10a2 + -21y2) = 0

Combine like terms: -14ay + 15ay = 1ay
(1ay + 10a2 + -21y2) = 0

Solving
1ay + 10a2 + -21y2 = 0

Solving for variable 'a'.

Factor a trinomial.
(5a + -7y)(2a + 3y) = 0


Subproblem 1
Set the factor '(5a + -7y)' equal to zero and attempt to solve:

Simplifying
5a + -7y = 0

Solving
5a + -7y = 0

Move all terms containing a to the left, all other terms to the right.

Add '7y' to each side of the equation.
5a + -7y + 7y = 0 + 7y

Combine like terms: -7y + 7y = 0
5a + 0 = 0 + 7y
5a = 0 + 7y
Remove the zero:
5a = 7y

Divide each side by '5'.
a = 1.4y

Simplifying
a = 1.4y

Subproblem 2
Set the factor '(2a + 3y)' equal to zero and attempt to solve:

Simplifying
2a + 3y = 0

Solving
2a + 3y = 0

Move all terms containing a to the left, all other terms to the right.

Add '-3y' to each side of the equation.
2a + 3y + -3y = 0 + -3y

Combine like terms: 3y + -3y = 0
2a + 0 = 0 + -3y
2a = 0 + -3y
Remove the zero:
2a = -3y

Divide each side by '2'.
a = -1.5y

Simplifying
a = -1.5y
Solution
a = {1.4y, -1.5y}

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