2x+14=49+14x+x^2

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Solution for 2x+14=49+14x+x^2 equation:


Simplifying
2x + 14 = 49 + 14x + x2

Reorder the terms:
14 + 2x = 49 + 14x + x2

Solving
14 + 2x = 49 + 14x + x2

Solving for variable 'x'.

Reorder the terms:
14 + -49 + 2x + -14x + -1x2 = 49 + 14x + x2 + -49 + -14x + -1x2

Combine like terms: 14 + -49 = -35
-35 + 2x + -14x + -1x2 = 49 + 14x + x2 + -49 + -14x + -1x2

Combine like terms: 2x + -14x = -12x
-35 + -12x + -1x2 = 49 + 14x + x2 + -49 + -14x + -1x2

Reorder the terms:
-35 + -12x + -1x2 = 49 + -49 + 14x + -14x + x2 + -1x2

Combine like terms: 49 + -49 = 0
-35 + -12x + -1x2 = 0 + 14x + -14x + x2 + -1x2
-35 + -12x + -1x2 = 14x + -14x + x2 + -1x2

Combine like terms: 14x + -14x = 0
-35 + -12x + -1x2 = 0 + x2 + -1x2
-35 + -12x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-35 + -12x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(35 + 12x + x2) = 0

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

Ignore the factor -1.

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 '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

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

Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5
Solution
x = {-7, -5}

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