x+y-y=4-(-x^2+8x-10)

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Solution for x+y-y=4-(-x^2+8x-10) equation: 


Simplifying
x + y + -1y = 4 + -1(-1x2 + 8x + -10)

Combine like terms: y + -1y = 0
x + 0 = 4 + -1(-1x2 + 8x + -10)
x = 4 + -1(-1x2 + 8x + -10)

Reorder the terms:
x = 4 + -1(-10 + 8x + -1x2)
x = 4 + (-10 * -1 + 8x * -1 + -1x2 * -1)
x = 4 + (10 + -8x + 1x2)

Combine like terms: 4 + 10 = 14
x = 14 + -8x + 1x2

Solving
x = 14 + -8x + 1x2

Solving for variable 'x'.

Reorder the terms:
-14 + x + 8x + -1x2 = 14 + -8x + 1x2 + -14 + 8x + -1x2

Combine like terms: x + 8x = 9x
-14 + 9x + -1x2 = 14 + -8x + 1x2 + -14 + 8x + -1x2

Reorder the terms:
-14 + 9x + -1x2 = 14 + -14 + -8x + 8x + 1x2 + -1x2

Combine like terms: 14 + -14 = 0
-14 + 9x + -1x2 = 0 + -8x + 8x + 1x2 + -1x2
-14 + 9x + -1x2 = -8x + 8x + 1x2 + -1x2

Combine like terms: -8x + 8x = 0
-14 + 9x + -1x2 = 0 + 1x2 + -1x2
-14 + 9x + -1x2 = 1x2 + -1x2

Combine like terms: 1x2 + -1x2 = 0
-14 + 9x + -1x2 = 0

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


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

Simplifying
-7 + x = 0

Solving
-7 + x = 0

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

Add '7' to each side of the equation.
-7 + 7 + x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + x = 0 + 7
x = 0 + 7

Combine like terms: 0 + 7 = 7
x = 7

Simplifying
x = 7

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

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

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

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

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

Simplifying
x = 2
Solution
x = {7, 2}

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