2x+12=-x^2+10x+5

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Solution for 2x+12=-x^2+10x+5 equation: 


Simplifying
2x + 12 = -1x2 + 10x + 5

Reorder the terms:
12 + 2x = -1x2 + 10x + 5

Reorder the terms:
12 + 2x = 5 + 10x + -1x2

Solving
12 + 2x = 5 + 10x + -1x2

Solving for variable 'x'.

Reorder the terms:
12 + -5 + 2x + -10x + x2 = 5 + 10x + -1x2 + -5 + -10x + x2

Combine like terms: 12 + -5 = 7
7 + 2x + -10x + x2 = 5 + 10x + -1x2 + -5 + -10x + x2

Combine like terms: 2x + -10x = -8x
7 + -8x + x2 = 5 + 10x + -1x2 + -5 + -10x + x2

Reorder the terms:
7 + -8x + x2 = 5 + -5 + 10x + -10x + -1x2 + x2

Combine like terms: 5 + -5 = 0
7 + -8x + x2 = 0 + 10x + -10x + -1x2 + x2
7 + -8x + x2 = 10x + -10x + -1x2 + x2

Combine like terms: 10x + -10x = 0
7 + -8x + x2 = 0 + -1x2 + x2
7 + -8x + x2 = -1x2 + x2

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

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


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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1

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

Simplifying
7 + -1x = 0

Solving
7 + -1x = 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 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {1, 7}

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