(10y-15)(5y+12)=0

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Solution for (10y-15)(5y+12)=0 equation: 


Simplifying
(10y + -15)(5y + 12) = 0

Reorder the terms:
(-15 + 10y)(5y + 12) = 0

Reorder the terms:
(-15 + 10y)(12 + 5y) = 0

Multiply (-15 + 10y) * (12 + 5y)
(-15(12 + 5y) + 10y * (12 + 5y)) = 0
((12 * -15 + 5y * -15) + 10y * (12 + 5y)) = 0
((-180 + -75y) + 10y * (12 + 5y)) = 0
(-180 + -75y + (12 * 10y + 5y * 10y)) = 0
(-180 + -75y + (120y + 50y2)) = 0

Combine like terms: -75y + 120y = 45y
(-180 + 45y + 50y2) = 0

Solving
-180 + 45y + 50y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-36 + 9y + 10y2) = 0

Factor a trinomial.
5((-12 + -5y)(3 + -2y)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-12 + -5y)' equal to zero and attempt to solve:

Simplifying
-12 + -5y = 0

Solving
-12 + -5y = 0

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

Add '12' to each side of the equation.
-12 + 12 + -5y = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -5y = 0 + 12
-5y = 0 + 12

Combine like terms: 0 + 12 = 12
-5y = 12

Divide each side by '-5'.
y = -2.4

Simplifying
y = -2.4

Subproblem 2
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
Solution
y = {-2.4, 1.5}

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