2y^2-28-7y=y^2-4y

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Solution for 2y^2-28-7y=y^2-4y equation:


Simplifying
2y2 + -28 + -7y = y2 + -4y

Reorder the terms:
-28 + -7y + 2y2 = y2 + -4y

Reorder the terms:
-28 + -7y + 2y2 = -4y + y2

Solving
-28 + -7y + 2y2 = -4y + y2

Solving for variable 'y'.

Reorder the terms:
-28 + -7y + 4y + 2y2 + -1y2 = -4y + y2 + 4y + -1y2

Combine like terms: -7y + 4y = -3y
-28 + -3y + 2y2 + -1y2 = -4y + y2 + 4y + -1y2

Combine like terms: 2y2 + -1y2 = 1y2
-28 + -3y + 1y2 = -4y + y2 + 4y + -1y2

Reorder the terms:
-28 + -3y + 1y2 = -4y + 4y + y2 + -1y2

Combine like terms: -4y + 4y = 0
-28 + -3y + 1y2 = 0 + y2 + -1y2
-28 + -3y + 1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-28 + -3y + 1y2 = 0

Factor a trinomial.
(-4 + -1y)(7 + -1y) = 0


Subproblem 1
Set the factor '(-4 + -1y)' equal to zero and attempt to solve:

Simplifying
-4 + -1y = 0

Solving
-4 + -1y = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1y = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1y = 0 + 4
-1y = 0 + 4

Combine like terms: 0 + 4 = 4
-1y = 4

Divide each side by '-1'.
y = -4

Simplifying
y = -4

Subproblem 2
Set the factor '(7 + -1y)' equal to zero and attempt to solve:

Simplifying
7 + -1y = 0

Solving
7 + -1y = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1y = 0 + -7
-1y = 0 + -7

Combine like terms: 0 + -7 = -7
-1y = -7

Divide each side by '-1'.
y = 7

Simplifying
y = 7
Solution
y = {-4, 7}

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