x^2+x^2+14x+49=4x^2+4x+1

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Solution for x^2+x^2+14x+49=4x^2+4x+1 equation: 


Simplifying
x2 + x2 + 14x + 49 = 4x2 + 4x + 1

Reorder the terms:
49 + 14x + x2 + x2 = 4x2 + 4x + 1

Combine like terms: x2 + x2 = 2x2
49 + 14x + 2x2 = 4x2 + 4x + 1

Reorder the terms:
49 + 14x + 2x2 = 1 + 4x + 4x2

Solving
49 + 14x + 2x2 = 1 + 4x + 4x2

Solving for variable 'x'.

Reorder the terms:
49 + -1 + 14x + -4x + 2x2 + -4x2 = 1 + 4x + 4x2 + -1 + -4x + -4x2

Combine like terms: 49 + -1 = 48
48 + 14x + -4x + 2x2 + -4x2 = 1 + 4x + 4x2 + -1 + -4x + -4x2

Combine like terms: 14x + -4x = 10x
48 + 10x + 2x2 + -4x2 = 1 + 4x + 4x2 + -1 + -4x + -4x2

Combine like terms: 2x2 + -4x2 = -2x2
48 + 10x + -2x2 = 1 + 4x + 4x2 + -1 + -4x + -4x2

Reorder the terms:
48 + 10x + -2x2 = 1 + -1 + 4x + -4x + 4x2 + -4x2

Combine like terms: 1 + -1 = 0
48 + 10x + -2x2 = 0 + 4x + -4x + 4x2 + -4x2
48 + 10x + -2x2 = 4x + -4x + 4x2 + -4x2

Combine like terms: 4x + -4x = 0
48 + 10x + -2x2 = 0 + 4x2 + -4x2
48 + 10x + -2x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
48 + 10x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(24 + 5x + -1x2) = 0

Factor a trinomial.
2((8 + -1x)(3 + x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

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

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

Divide each side by '-1'.
x = 8

Simplifying
x = 8

Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {8, -3}

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