(2y+3)(7y-4)=0

Solution for (2y+3)(7y-4)=0 equation:

Simplifying
(2y + 3)(7y + -4) = 0

Reorder the terms:
(3 + 2y)(7y + -4) = 0

Reorder the terms:
(3 + 2y)(-4 + 7y) = 0

Multiply (3 + 2y) * (-4 + 7y)
(3(-4 + 7y) + 2y * (-4 + 7y)) = 0
((-4 * 3 + 7y * 3) + 2y * (-4 + 7y)) = 0
((-12 + 21y) + 2y * (-4 + 7y)) = 0
(-12 + 21y + (-4 * 2y + 7y * 2y)) = 0
(-12 + 21y + (-8y + 14y2)) = 0

Combine like terms: 21y + -8y = 13y
(-12 + 13y + 14y2) = 0

Solving
-12 + 13y + 14y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-3 + -2y)(4 + -7y) = 0

Subproblem 1
Set the factor '(-3 + -2y)' equal to zero and attempt to solve:

Simplifying
-3 + -2y = 0

Solving
-3 + -2y = 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 + -2y = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2y = 0 + 3
-2y = 0 + 3

Combine like terms: 0 + 3 = 3
-2y = 3

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

Simplifying
y = -1.5
Subproblem 2
Set the factor '(4 + -7y)' equal to zero and attempt to solve:

Simplifying
4 + -7y = 0

Solving
4 + -7y = 0

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

Add '-4' to each side of the equation.
4 + -4 + -7y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -7y = 0 + -4
-7y = 0 + -4

Combine like terms: 0 + -4 = -4
-7y = -4

Divide each side by '-7'.
y = 0.5714285714

Simplifying
y = 0.5714285714
Solution
y = {-1.5, 0.5714285714}