(2x+6)(6x-2)=0

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Solution for (2x+6)(6x-2)=0 equation: 


Simplifying
(2x + 6)(6x + -2) = 0

Reorder the terms:
(6 + 2x)(6x + -2) = 0

Reorder the terms:
(6 + 2x)(-2 + 6x) = 0

Multiply (6 + 2x) * (-2 + 6x)
(6(-2 + 6x) + 2x * (-2 + 6x)) = 0
((-2 * 6 + 6x * 6) + 2x * (-2 + 6x)) = 0
((-12 + 36x) + 2x * (-2 + 6x)) = 0
(-12 + 36x + (-2 * 2x + 6x * 2x)) = 0
(-12 + 36x + (-4x + 12x2)) = 0

Combine like terms: 36x + -4x = 32x
(-12 + 32x + 12x2) = 0

Solving
-12 + 32x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-3 + 8x + 3x2) = 0

Factor a trinomial.
4((-3 + -1x)(1 + -3x)) = 0

Ignore the factor 4.

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

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

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

Simplifying
1 + -3x = 0

Solving
1 + -3x = 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 + -3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3x = 0 + -1
-3x = 0 + -1

Combine like terms: 0 + -1 = -1
-3x = -1

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Solution
x = {-3, 0.3333333333}

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