=(5y-3)(2y-7)

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Solution for =(5y-3)(2y-7) equation: 


Simplifying
0 = (5y + -3)(2y + -7)

Reorder the terms:
0 = (-3 + 5y)(2y + -7)

Reorder the terms:
0 = (-3 + 5y)(-7 + 2y)

Multiply (-3 + 5y) * (-7 + 2y)
0 = (-3(-7 + 2y) + 5y * (-7 + 2y))
0 = ((-7 * -3 + 2y * -3) + 5y * (-7 + 2y))
0 = ((21 + -6y) + 5y * (-7 + 2y))
0 = (21 + -6y + (-7 * 5y + 2y * 5y))
0 = (21 + -6y + (-35y + 10y2))

Combine like terms: -6y + -35y = -41y
0 = (21 + -41y + 10y2)

Solving
0 = 21 + -41y + 10y2

Solving for variable 'y'.

Combine like terms: 0 + -21 = -21
-21 + 41y + -10y2 = 21 + -41y + 10y2 + -21 + 41y + -10y2

Reorder the terms:
-21 + 41y + -10y2 = 21 + -21 + -41y + 41y + 10y2 + -10y2

Combine like terms: 21 + -21 = 0
-21 + 41y + -10y2 = 0 + -41y + 41y + 10y2 + -10y2
-21 + 41y + -10y2 = -41y + 41y + 10y2 + -10y2

Combine like terms: -41y + 41y = 0
-21 + 41y + -10y2 = 0 + 10y2 + -10y2
-21 + 41y + -10y2 = 10y2 + -10y2

Combine like terms: 10y2 + -10y2 = 0
-21 + 41y + -10y2 = 0

Factor a trinomial.
(-7 + 2y)(3 + -5y) = 0


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

Simplifying
-7 + 2y = 0

Solving
-7 + 2y = 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 + 2y = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 2y = 0 + 7
2y = 0 + 7

Combine like terms: 0 + 7 = 7
2y = 7

Divide each side by '2'.
y = 3.5

Simplifying
y = 3.5

Subproblem 2
Set the factor '(3 + -5y)' equal to zero and attempt to solve:

Simplifying
3 + -5y = 0

Solving
3 + -5y = 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 + -5y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5y = 0 + -3
-5y = 0 + -3

Combine like terms: 0 + -3 = -3
-5y = -3

Divide each side by '-5'.
y = 0.6

Simplifying
y = 0.6
Solution
y = {3.5, 0.6}

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