6x^2+113x+399=3x^2+71x+252

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Solution for 6x^2+113x+399=3x^2+71x+252 equation: 


Simplifying
6x2 + 113x + 399 = 3x2 + 71x + 252

Reorder the terms:
399 + 113x + 6x2 = 3x2 + 71x + 252

Reorder the terms:
399 + 113x + 6x2 = 252 + 71x + 3x2

Solving
399 + 113x + 6x2 = 252 + 71x + 3x2

Solving for variable 'x'.

Reorder the terms:
399 + -252 + 113x + -71x + 6x2 + -3x2 = 252 + 71x + 3x2 + -252 + -71x + -3x2

Combine like terms: 399 + -252 = 147
147 + 113x + -71x + 6x2 + -3x2 = 252 + 71x + 3x2 + -252 + -71x + -3x2

Combine like terms: 113x + -71x = 42x
147 + 42x + 6x2 + -3x2 = 252 + 71x + 3x2 + -252 + -71x + -3x2

Combine like terms: 6x2 + -3x2 = 3x2
147 + 42x + 3x2 = 252 + 71x + 3x2 + -252 + -71x + -3x2

Reorder the terms:
147 + 42x + 3x2 = 252 + -252 + 71x + -71x + 3x2 + -3x2

Combine like terms: 252 + -252 = 0
147 + 42x + 3x2 = 0 + 71x + -71x + 3x2 + -3x2
147 + 42x + 3x2 = 71x + -71x + 3x2 + -3x2

Combine like terms: 71x + -71x = 0
147 + 42x + 3x2 = 0 + 3x2 + -3x2
147 + 42x + 3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
147 + 42x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(49 + 14x + x2) = 0

Factor a trinomial.
3((7 + x)(7 + x)) = 0

Ignore the factor 3.

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 '(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
Solution
x = {-7, -7}

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