(2y+7)(5y-3y+6)=

Solution for (2y+7)(5y-3y+6)= equation:

Simplifying
(2y + 7)(5y + -3y + 6) = 0

Reorder the terms:
(7 + 2y)(5y + -3y + 6) = 0

Reorder the terms:
(7 + 2y)(6 + 5y + -3y) = 0

Combine like terms: 5y + -3y = 2y
(7 + 2y)(6 + 2y) = 0

Multiply (7 + 2y) * (6 + 2y)
(7(6 + 2y) + 2y * (6 + 2y)) = 0
((6 * 7 + 2y * 7) + 2y * (6 + 2y)) = 0
((42 + 14y) + 2y * (6 + 2y)) = 0
(42 + 14y + (6 * 2y + 2y * 2y)) = 0
(42 + 14y + (12y + 4y2)) = 0

Combine like terms: 14y + 12y = 26y
(42 + 26y + 4y2) = 0

Solving
42 + 26y + 4y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(21 + 13y + 2y2) = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor '(7 + 2y)' equal to zero and attempt to solve:

Simplifying
7 + 2y = 0

Solving
7 + 2y = 0

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

Add '-7' to each side of the equation.
7 + -7 + 2y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 2y = 0 + -7
2y = 0 + -7

Combine like terms: 0 + -7 = -7
2y = -7

Divide each side by '2'.
y = -3.5

Simplifying
y = -3.5
Subproblem 2
Set the factor '(3 + y)' equal to zero and attempt to solve:

Simplifying
3 + y = 0

Solving
3 + y = 0

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

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

Combine like terms: 3 + -3 = 0
0 + y = 0 + -3
y = 0 + -3

Combine like terms: 0 + -3 = -3
y = -3

Simplifying
y = -3
Solution
y = {-3.5, -3}