-5y(4y-3)=2(2-10y)+11

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Solution for -5y(4y-3)=2(2-10y)+11 equation: 


Simplifying
-5y(4y + -3) = 2(2 + -10y) + 11

Reorder the terms:
-5y(-3 + 4y) = 2(2 + -10y) + 11
(-3 * -5y + 4y * -5y) = 2(2 + -10y) + 11
(15y + -20y2) = 2(2 + -10y) + 11
15y + -20y2 = (2 * 2 + -10y * 2) + 11
15y + -20y2 = (4 + -20y) + 11

Reorder the terms:
15y + -20y2 = 4 + 11 + -20y

Combine like terms: 4 + 11 = 15
15y + -20y2 = 15 + -20y

Solving
15y + -20y2 = 15 + -20y

Solving for variable 'y'.

Reorder the terms:
-15 + 15y + 20y + -20y2 = 15 + -20y + -15 + 20y

Combine like terms: 15y + 20y = 35y
-15 + 35y + -20y2 = 15 + -20y + -15 + 20y

Reorder the terms:
-15 + 35y + -20y2 = 15 + -15 + -20y + 20y

Combine like terms: 15 + -15 = 0
-15 + 35y + -20y2 = 0 + -20y + 20y
-15 + 35y + -20y2 = -20y + 20y

Combine like terms: -20y + 20y = 0
-15 + 35y + -20y2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-3 + 7y + -4y2) = 0

Factor a trinomial.
5((-1 + y)(3 + -4y)) = 0

Ignore the factor 5.

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

Simplifying
-1 + y = 0

Solving
-1 + y = 0

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

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

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

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

Simplifying
y = 1

Subproblem 2
Set the factor '(3 + -4y)' equal to zero and attempt to solve:

Simplifying
3 + -4y = 0

Solving
3 + -4y = 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 + -4y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4y = 0 + -3
-4y = 0 + -3

Combine like terms: 0 + -3 = -3
-4y = -3

Divide each side by '-4'.
y = 0.75

Simplifying
y = 0.75
Solution
y = {1, 0.75}

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