16y^2-25-(-4y+5)(8y+15)=0

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Solution for 16y^2-25-(-4y+5)(8y+15)=0 equation: 


Simplifying
16y2 + -25 + -1(-4y + 5)(8y + 15) = 0

Reorder the terms:
16y2 + -25 + -1(5 + -4y)(8y + 15) = 0

Reorder the terms:
16y2 + -25 + -1(5 + -4y)(15 + 8y) = 0

Multiply (5 + -4y) * (15 + 8y)
16y2 + -25 + -1(5(15 + 8y) + -4y * (15 + 8y)) = 0
16y2 + -25 + -1((15 * 5 + 8y * 5) + -4y * (15 + 8y)) = 0
16y2 + -25 + -1((75 + 40y) + -4y * (15 + 8y)) = 0
16y2 + -25 + -1(75 + 40y + (15 * -4y + 8y * -4y)) = 0
16y2 + -25 + -1(75 + 40y + (-60y + -32y2)) = 0

Combine like terms: 40y + -60y = -20y
16y2 + -25 + -1(75 + -20y + -32y2) = 0
16y2 + -25 + (75 * -1 + -20y * -1 + -32y2 * -1) = 0
16y2 + -25 + (-75 + 20y + 32y2) = 0

Reorder the terms:
-25 + -75 + 20y + 16y2 + 32y2 = 0

Combine like terms: -25 + -75 = -100
-100 + 20y + 16y2 + 32y2 = 0

Combine like terms: 16y2 + 32y2 = 48y2
-100 + 20y + 48y2 = 0

Solving
-100 + 20y + 48y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-25 + 5y + 12y2) = 0

Factor a trinomial.
4((-5 + -3y)(5 + -4y)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-5 + -3y)' equal to zero and attempt to solve:

Simplifying
-5 + -3y = 0

Solving
-5 + -3y = 0

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

Add '5' to each side of the equation.
-5 + 5 + -3y = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3y = 0 + 5
-3y = 0 + 5

Combine like terms: 0 + 5 = 5
-3y = 5

Divide each side by '-3'.
y = -1.666666667

Simplifying
y = -1.666666667

Subproblem 2
Set the factor '(5 + -4y)' equal to zero and attempt to solve:

Simplifying
5 + -4y = 0

Solving
5 + -4y = 0

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

Add '-5' to each side of the equation.
5 + -5 + -4y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4y = 0 + -5
-4y = 0 + -5

Combine like terms: 0 + -5 = -5
-4y = -5

Divide each side by '-4'.
y = 1.25

Simplifying
y = 1.25
Solution
y = {-1.666666667, 1.25}

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