6y^2+11y-10=2y+5

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Solution for 6y^2+11y-10=2y+5 equation: 


Simplifying
6y2 + 11y + -10 = 2y + 5

Reorder the terms:
-10 + 11y + 6y2 = 2y + 5

Reorder the terms:
-10 + 11y + 6y2 = 5 + 2y

Solving
-10 + 11y + 6y2 = 5 + 2y

Solving for variable 'y'.

Reorder the terms:
-10 + -5 + 11y + -2y + 6y2 = 5 + 2y + -5 + -2y

Combine like terms: -10 + -5 = -15
-15 + 11y + -2y + 6y2 = 5 + 2y + -5 + -2y

Combine like terms: 11y + -2y = 9y
-15 + 9y + 6y2 = 5 + 2y + -5 + -2y

Reorder the terms:
-15 + 9y + 6y2 = 5 + -5 + 2y + -2y

Combine like terms: 5 + -5 = 0
-15 + 9y + 6y2 = 0 + 2y + -2y
-15 + 9y + 6y2 = 2y + -2y

Combine like terms: 2y + -2y = 0
-15 + 9y + 6y2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + 3y + 2y2) = 0

Factor a trinomial.
3((-5 + -2y)(1 + -1y)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-5 + -2y)' equal to zero and attempt to solve:

Simplifying
-5 + -2y = 0

Solving
-5 + -2y = 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 + -2y = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2y = 0 + 5
-2y = 0 + 5

Combine like terms: 0 + 5 = 5
-2y = 5

Divide each side by '-2'.
y = -2.5

Simplifying
y = -2.5

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

Simplifying
1 + -1y = 0

Solving
1 + -1y = 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 + -1y = 0 + -1

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

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

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

Simplifying
y = 1
Solution
y = {-2.5, 1}

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