x^2-5x+15=x+7

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Solution for x^2-5x+15=x+7 equation: 


Simplifying
x2 + -5x + 15 = x + 7

Reorder the terms:
15 + -5x + x2 = x + 7

Reorder the terms:
15 + -5x + x2 = 7 + x

Solving
15 + -5x + x2 = 7 + x

Solving for variable 'x'.

Reorder the terms:
15 + -7 + -5x + -1x + x2 = 7 + x + -7 + -1x

Combine like terms: 15 + -7 = 8
8 + -5x + -1x + x2 = 7 + x + -7 + -1x

Combine like terms: -5x + -1x = -6x
8 + -6x + x2 = 7 + x + -7 + -1x

Reorder the terms:
8 + -6x + x2 = 7 + -7 + x + -1x

Combine like terms: 7 + -7 = 0
8 + -6x + x2 = 0 + x + -1x
8 + -6x + x2 = x + -1x

Combine like terms: x + -1x = 0
8 + -6x + x2 = 0

Factor a trinomial.
(2 + -1x)(4 + -1x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {2, 4}

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