-7=-5y+4y(-y+9)-7(7+3y)

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Solution for -7=-5y+4y(-y+9)-7(7+3y) equation: 


Simplifying
-7 = -5y + 4y(-1y + 9) + -7(7 + 3y)

Reorder the terms:
-7 = -5y + 4y(9 + -1y) + -7(7 + 3y)
-7 = -5y + (9 * 4y + -1y * 4y) + -7(7 + 3y)
-7 = -5y + (36y + -4y2) + -7(7 + 3y)
-7 = -5y + 36y + -4y2 + (7 * -7 + 3y * -7)
-7 = -5y + 36y + -4y2 + (-49 + -21y)

Reorder the terms:
-7 = -49 + -5y + 36y + -21y + -4y2

Combine like terms: -5y + 36y = 31y
-7 = -49 + 31y + -21y + -4y2

Combine like terms: 31y + -21y = 10y
-7 = -49 + 10y + -4y2

Solving
-7 = -49 + 10y + -4y2

Solving for variable 'y'.

Combine like terms: -7 + 49 = 42
42 + -10y + 4y2 = -49 + 10y + -4y2 + 49 + -10y + 4y2

Reorder the terms:
42 + -10y + 4y2 = -49 + 49 + 10y + -10y + -4y2 + 4y2

Combine like terms: -49 + 49 = 0
42 + -10y + 4y2 = 0 + 10y + -10y + -4y2 + 4y2
42 + -10y + 4y2 = 10y + -10y + -4y2 + 4y2

Combine like terms: 10y + -10y = 0
42 + -10y + 4y2 = 0 + -4y2 + 4y2
42 + -10y + 4y2 = -4y2 + 4y2

Combine like terms: -4y2 + 4y2 = 0
42 + -10y + 4y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(21 + -5y + 2y2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(21 + -5y + 2y2)' equal to zero and attempt to solve:

Simplifying
21 + -5y + 2y2 = 0

Solving
21 + -5y + 2y2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
10.5 + -2.5y + y2 = 0

Move the constant term to the right:

Add '-10.5' to each side of the equation.
10.5 + -2.5y + -10.5 + y2 = 0 + -10.5

Reorder the terms:
10.5 + -10.5 + -2.5y + y2 = 0 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + -2.5y + y2 = 0 + -10.5
-2.5y + y2 = 0 + -10.5

Combine like terms: 0 + -10.5 = -10.5
-2.5y + y2 = -10.5

The y term is -2.5y.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5y + 1.5625 + y2 = -10.5 + 1.5625

Reorder the terms:
1.5625 + -2.5y + y2 = -10.5 + 1.5625

Combine like terms: -10.5 + 1.5625 = -8.9375
1.5625 + -2.5y + y2 = -8.9375

Factor a perfect square on the left side:
(y + -1.25)(y + -1.25) = -8.9375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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