7y-1=2y(y+3)-2

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Solution for 7y-1=2y(y+3)-2 equation:


Simplifying
7y + -1 = 2y(y + 3) + -2

Reorder the terms:
-1 + 7y = 2y(y + 3) + -2

Reorder the terms:
-1 + 7y = 2y(3 + y) + -2
-1 + 7y = (3 * 2y + y * 2y) + -2
-1 + 7y = (6y + 2y2) + -2

Reorder the terms:
-1 + 7y = -2 + 6y + 2y2

Solving
-1 + 7y = -2 + 6y + 2y2

Solving for variable 'y'.

Reorder the terms:
-1 + 2 + 7y + -6y + -2y2 = -2 + 6y + 2y2 + 2 + -6y + -2y2

Combine like terms: -1 + 2 = 1
1 + 7y + -6y + -2y2 = -2 + 6y + 2y2 + 2 + -6y + -2y2

Combine like terms: 7y + -6y = 1y
1 + 1y + -2y2 = -2 + 6y + 2y2 + 2 + -6y + -2y2

Reorder the terms:
1 + 1y + -2y2 = -2 + 2 + 6y + -6y + 2y2 + -2y2

Combine like terms: -2 + 2 = 0
1 + 1y + -2y2 = 0 + 6y + -6y + 2y2 + -2y2
1 + 1y + -2y2 = 6y + -6y + 2y2 + -2y2

Combine like terms: 6y + -6y = 0
1 + 1y + -2y2 = 0 + 2y2 + -2y2
1 + 1y + -2y2 = 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
1 + 1y + -2y2 = 0

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

Subproblem 1

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

Subproblem 2

Set the factor '(1 + 2y)' equal to zero and attempt to solve: Simplifying 1 + 2y = 0 Solving 1 + 2y = 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 + 2y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2y = 0 + -1 2y = 0 + -1 Combine like terms: 0 + -1 = -1 2y = -1 Divide each side by '2'. y = -0.5 Simplifying y = -0.5

Solution

y = {1, -0.5}

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