5y^2-3(y-7)=35

Solution for 5y^2-3(y-7)=35 equation:

Simplifying
5y2 + -3(y + -7) = 35

Reorder the terms:
5y2 + -3(-7 + y) = 35
5y2 + (-7 * -3 + y * -3) = 35
5y2 + (21 + -3y) = 35

Reorder the terms:
21 + -3y + 5y2 = 35

Solving
21 + -3y + 5y2 = 35

Solving for variable 'y'.

Reorder the terms:
21 + -35 + -3y + 5y2 = 35 + -35

Combine like terms: 21 + -35 = -14
-14 + -3y + 5y2 = 35 + -35

Combine like terms: 35 + -35 = 0
-14 + -3y + 5y2 = 0

Factor a trinomial.
(-7 + -5y)(2 + -1y) = 0

Subproblem 1
Set the factor '(-7 + -5y)' equal to zero and attempt to solve:

Simplifying
-7 + -5y = 0

Solving
-7 + -5y = 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 + -5y = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -5y = 0 + 7
-5y = 0 + 7

Combine like terms: 0 + 7 = 7
-5y = 7

Divide each side by '-5'.
y = -1.4

Simplifying
y = -1.4
Subproblem 2
Set the factor '(2 + -1y)' equal to zero and attempt to solve:

Simplifying
2 + -1y = 0

Solving
2 + -1y = 0

Move all terms containing y to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -1y = 0 + -2

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

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

Divide each side by '-1'.
y = 2

Simplifying
y = 2
Solution
y = {-1.4, 2}