6+2x=(-14+2x)(-14+2x)

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Solution for 6+2x=(-14+2x)(-14+2x) equation: 


Simplifying
6 + 2x = (-14 + 2x)(-14 + 2x)

Multiply (-14 + 2x) * (-14 + 2x)
6 + 2x = (-14(-14 + 2x) + 2x * (-14 + 2x))
6 + 2x = ((-14 * -14 + 2x * -14) + 2x * (-14 + 2x))
6 + 2x = ((196 + -28x) + 2x * (-14 + 2x))
6 + 2x = (196 + -28x + (-14 * 2x + 2x * 2x))
6 + 2x = (196 + -28x + (-28x + 4x2))

Combine like terms: -28x + -28x = -56x
6 + 2x = (196 + -56x + 4x2)

Solving
6 + 2x = 196 + -56x + 4x2

Solving for variable 'x'.

Reorder the terms:
6 + -196 + 2x + 56x + -4x2 = 196 + -56x + 4x2 + -196 + 56x + -4x2

Combine like terms: 6 + -196 = -190
-190 + 2x + 56x + -4x2 = 196 + -56x + 4x2 + -196 + 56x + -4x2

Combine like terms: 2x + 56x = 58x
-190 + 58x + -4x2 = 196 + -56x + 4x2 + -196 + 56x + -4x2

Reorder the terms:
-190 + 58x + -4x2 = 196 + -196 + -56x + 56x + 4x2 + -4x2

Combine like terms: 196 + -196 = 0
-190 + 58x + -4x2 = 0 + -56x + 56x + 4x2 + -4x2
-190 + 58x + -4x2 = -56x + 56x + 4x2 + -4x2

Combine like terms: -56x + 56x = 0
-190 + 58x + -4x2 = 0 + 4x2 + -4x2
-190 + 58x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-190 + 58x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-95 + 29x + -2x2) = 0

Factor a trinomial.
2((-19 + 2x)(5 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-19 + 2x)' equal to zero and attempt to solve:

Simplifying
-19 + 2x = 0

Solving
-19 + 2x = 0

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

Add '19' to each side of the equation.
-19 + 19 + 2x = 0 + 19

Combine like terms: -19 + 19 = 0
0 + 2x = 0 + 19
2x = 0 + 19

Combine like terms: 0 + 19 = 19
2x = 19

Divide each side by '2'.
x = 9.5

Simplifying
x = 9.5

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {9.5, 5}

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