(X-3)(X+3)=6x^2-14

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Solution for (X-3)(X+3)=6x^2-14 equation: 


Simplifying
(X + -3)(X + 3) = 6x2 + -14

Reorder the terms:
(-3 + X)(X + 3) = 6x2 + -14

Reorder the terms:
(-3 + X)(3 + X) = 6x2 + -14

Multiply (-3 + X) * (3 + X)
(-3(3 + X) + X(3 + X)) = 6x2 + -14
((3 * -3 + X * -3) + X(3 + X)) = 6x2 + -14
((-9 + -3X) + X(3 + X)) = 6x2 + -14
(-9 + -3X + (3 * X + X * X)) = 6x2 + -14
(-9 + -3X + (3X + X2)) = 6x2 + -14

Combine like terms: -3X + 3X = 0
(-9 + 0 + X2) = 6x2 + -14
(-9 + X2) = 6x2 + -14

Reorder the terms:
-9 + X2 = -14 + 6x2

Solving
-9 + X2 = -14 + 6x2

Solving for variable 'X'.

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

Add '9' to each side of the equation.
-9 + 9 + X2 = -14 + 9 + 6x2

Combine like terms: -9 + 9 = 0
0 + X2 = -14 + 9 + 6x2
X2 = -14 + 9 + 6x2

Combine like terms: -14 + 9 = -5
X2 = -5 + 6x2

Simplifying
X2 = -5 + 6x2

Reorder the terms:
5 + X2 + -6x2 = -5 + 6x2 + 5 + -6x2

Reorder the terms:
5 + X2 + -6x2 = -5 + 5 + 6x2 + -6x2

Combine like terms: -5 + 5 = 0
5 + X2 + -6x2 = 0 + 6x2 + -6x2
5 + X2 + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
5 + X2 + -6x2 = 0

Factor a trinomial.
(X + -1x)(X + 6x) = 0


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

Simplifying
X + -1x = 0

Solving
X + -1x = 0

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

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

Combine like terms: -1x + x = 0
X + 0 = 0 + x
X = 0 + x
Remove the zero:
X = x

Simplifying
X = x

Subproblem 2
Set the factor '(X + 6x)' equal to zero and attempt to solve:

Simplifying
X + 6x = 0

Solving
X + 6x = 0

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

Add '-6x' to each side of the equation.
X + 6x + -6x = 0 + -6x

Combine like terms: 6x + -6x = 0
X + 0 = 0 + -6x
X = 0 + -6x
Remove the zero:
X = -6x

Simplifying
X = -6x
Solution
X = {x, -6x}

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