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

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


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

Multiply (-6 + 2x) * (-6 + 2x)
14 + 2x = (-6(-6 + 2x) + 2x * (-6 + 2x))
14 + 2x = ((-6 * -6 + 2x * -6) + 2x * (-6 + 2x))
14 + 2x = ((36 + -12x) + 2x * (-6 + 2x))
14 + 2x = (36 + -12x + (-6 * 2x + 2x * 2x))
14 + 2x = (36 + -12x + (-12x + 4x2))

Combine like terms: -12x + -12x = -24x
14 + 2x = (36 + -24x + 4x2)

Solving
14 + 2x = 36 + -24x + 4x2

Solving for variable 'x'.

Reorder the terms:
14 + -36 + 2x + 24x + -4x2 = 36 + -24x + 4x2 + -36 + 24x + -4x2

Combine like terms: 14 + -36 = -22
-22 + 2x + 24x + -4x2 = 36 + -24x + 4x2 + -36 + 24x + -4x2

Combine like terms: 2x + 24x = 26x
-22 + 26x + -4x2 = 36 + -24x + 4x2 + -36 + 24x + -4x2

Reorder the terms:
-22 + 26x + -4x2 = 36 + -36 + -24x + 24x + 4x2 + -4x2

Combine like terms: 36 + -36 = 0
-22 + 26x + -4x2 = 0 + -24x + 24x + 4x2 + -4x2
-22 + 26x + -4x2 = -24x + 24x + 4x2 + -4x2

Combine like terms: -24x + 24x = 0
-22 + 26x + -4x2 = 0 + 4x2 + -4x2
-22 + 26x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-22 + 26x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-11 + 13x + -2x2) = 0

Factor a trinomial.
2((-11 + 2x)(1 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-11 + 2x)' equal to zero and attempt to solve:

Simplifying
-11 + 2x = 0

Solving
-11 + 2x = 0

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

Add '11' to each side of the equation.
-11 + 11 + 2x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + 2x = 0 + 11
2x = 0 + 11

Combine like terms: 0 + 11 = 11
2x = 11

Divide each side by '2'.
x = 5.5

Simplifying
x = 5.5

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {5.5, 1}

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