=(3y+7)(4y+5)

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Solution for =(3y+7)(4y+5) equation: 


Simplifying
0 = (3y + 7)(4y + 5)

Reorder the terms:
0 = (7 + 3y)(4y + 5)

Reorder the terms:
0 = (7 + 3y)(5 + 4y)

Multiply (7 + 3y) * (5 + 4y)
0 = (7(5 + 4y) + 3y * (5 + 4y))
0 = ((5 * 7 + 4y * 7) + 3y * (5 + 4y))
0 = ((35 + 28y) + 3y * (5 + 4y))
0 = (35 + 28y + (5 * 3y + 4y * 3y))
0 = (35 + 28y + (15y + 12y2))

Combine like terms: 28y + 15y = 43y
0 = (35 + 43y + 12y2)

Solving
0 = 35 + 43y + 12y2

Solving for variable 'y'.

Combine like terms: 0 + -35 = -35
-35 + -43y + -12y2 = 35 + 43y + 12y2 + -35 + -43y + -12y2

Reorder the terms:
-35 + -43y + -12y2 = 35 + -35 + 43y + -43y + 12y2 + -12y2

Combine like terms: 35 + -35 = 0
-35 + -43y + -12y2 = 0 + 43y + -43y + 12y2 + -12y2
-35 + -43y + -12y2 = 43y + -43y + 12y2 + -12y2

Combine like terms: 43y + -43y = 0
-35 + -43y + -12y2 = 0 + 12y2 + -12y2
-35 + -43y + -12y2 = 12y2 + -12y2

Combine like terms: 12y2 + -12y2 = 0
-35 + -43y + -12y2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(35 + 43y + 12y2) = 0

Factor a trinomial.
-1((7 + 3y)(5 + 4y)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(7 + 3y)' equal to zero and attempt to solve:

Simplifying
7 + 3y = 0

Solving
7 + 3y = 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 + 3y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3y = 0 + -7
3y = 0 + -7

Combine like terms: 0 + -7 = -7
3y = -7

Divide each side by '3'.
y = -2.333333333

Simplifying
y = -2.333333333

Subproblem 2
Set the factor '(5 + 4y)' equal to zero and attempt to solve:

Simplifying
5 + 4y = 0

Solving
5 + 4y = 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 + 4y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4y = 0 + -5
4y = 0 + -5

Combine like terms: 0 + -5 = -5
4y = -5

Divide each side by '4'.
y = -1.25

Simplifying
y = -1.25
Solution
y = {-2.333333333, -1.25}

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