6x^2+6x+6=14x+14

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Solution for 6x^2+6x+6=14x+14 equation:


Simplifying
6x2 + 6x + 6 = 14x + 14

Reorder the terms:
6 + 6x + 6x2 = 14x + 14

Reorder the terms:
6 + 6x + 6x2 = 14 + 14x

Solving
6 + 6x + 6x2 = 14 + 14x

Solving for variable 'x'.

Reorder the terms:
6 + -14 + 6x + -14x + 6x2 = 14 + 14x + -14 + -14x

Combine like terms: 6 + -14 = -8
-8 + 6x + -14x + 6x2 = 14 + 14x + -14 + -14x

Combine like terms: 6x + -14x = -8x
-8 + -8x + 6x2 = 14 + 14x + -14 + -14x

Reorder the terms:
-8 + -8x + 6x2 = 14 + -14 + 14x + -14x

Combine like terms: 14 + -14 = 0
-8 + -8x + 6x2 = 0 + 14x + -14x
-8 + -8x + 6x2 = 14x + -14x

Combine like terms: 14x + -14x = 0
-8 + -8x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + -4x + 3x2) = 0

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

Ignore the factor 2.

Subproblem 1
Set the factor '(-2 + -3x)' equal to zero and attempt to solve:

Simplifying
-2 + -3x = 0

Solving
-2 + -3x = 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 + -3x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3x = 0 + 2
-3x = 0 + 2

Combine like terms: 0 + 2 = 2
-3x = 2

Divide each side by '-3'.
x = -0.6666666667

Simplifying
x = -0.6666666667

Subproblem 2
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
Solution
x = {-0.6666666667, 2}

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