(y-10)(2y+3)=0

Solution for (y-10)(2y+3)=0 equation:

Simplifying
(y + -10)(2y + 3) = 0

Reorder the terms:
(-10 + y)(2y + 3) = 0

Reorder the terms:
(-10 + y)(3 + 2y) = 0

Multiply (-10 + y) * (3 + 2y)
(-10(3 + 2y) + y(3 + 2y)) = 0
((3 * -10 + 2y * -10) + y(3 + 2y)) = 0
((-30 + -20y) + y(3 + 2y)) = 0
(-30 + -20y + (3 * y + 2y * y)) = 0
(-30 + -20y + (3y + 2y2)) = 0

Combine like terms: -20y + 3y = -17y
(-30 + -17y + 2y2) = 0

Solving
-30 + -17y + 2y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-3 + -2y)(10 + -1y) = 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 '(10 + -1y)' equal to zero and attempt to solve:

Simplifying
10 + -1y = 0

Solving
10 + -1y = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1y = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1y = 0 + -10
-1y = 0 + -10

Combine like terms: 0 + -10 = -10
-1y = -10

Divide each side by '-1'.
y = 10

Simplifying
y = 10
Solution
y = {-1.5, 10}