7y+7=-4y^2+12y+16+3y-12

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Solution for 7y+7=-4y^2+12y+16+3y-12 equation:


Simplifying
7y + 7 = -4y2 + 12y + 16 + 3y + -12

Reorder the terms:
7 + 7y = -4y2 + 12y + 16 + 3y + -12

Reorder the terms:
7 + 7y = 16 + -12 + 12y + 3y + -4y2

Combine like terms: 16 + -12 = 4
7 + 7y = 4 + 12y + 3y + -4y2

Combine like terms: 12y + 3y = 15y
7 + 7y = 4 + 15y + -4y2

Solving
7 + 7y = 4 + 15y + -4y2

Solving for variable 'y'.

Reorder the terms:
7 + -4 + 7y + -15y + 4y2 = 4 + 15y + -4y2 + -4 + -15y + 4y2

Combine like terms: 7 + -4 = 3
3 + 7y + -15y + 4y2 = 4 + 15y + -4y2 + -4 + -15y + 4y2

Combine like terms: 7y + -15y = -8y
3 + -8y + 4y2 = 4 + 15y + -4y2 + -4 + -15y + 4y2

Reorder the terms:
3 + -8y + 4y2 = 4 + -4 + 15y + -15y + -4y2 + 4y2

Combine like terms: 4 + -4 = 0
3 + -8y + 4y2 = 0 + 15y + -15y + -4y2 + 4y2
3 + -8y + 4y2 = 15y + -15y + -4y2 + 4y2

Combine like terms: 15y + -15y = 0
3 + -8y + 4y2 = 0 + -4y2 + 4y2
3 + -8y + 4y2 = -4y2 + 4y2

Combine like terms: -4y2 + 4y2 = 0
3 + -8y + 4y2 = 0

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

Subproblem 1

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

Subproblem 2

Set the factor '(3 + -2y)' equal to zero and attempt to solve: Simplifying 3 + -2y = 0 Solving 3 + -2y = 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 + -2y = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2y = 0 + -3 -2y = 0 + -3 Combine like terms: 0 + -3 = -3 -2y = -3 Divide each side by '-2'. y = 1.5 Simplifying y = 1.5

Solution

y = {0.5, 1.5}

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