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

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


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

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

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

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

Combine like terms: -15y + -28y = -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 a trinomial.
(-7 + 3y)(5 + -4y) = 0


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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