(2X+3)(2X-6)=0

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Solution for (2X+3)(2X-6)=0 equation: 


Simplifying
(2X + 3)(2X + -6) = 0

Reorder the terms:
(3 + 2X)(2X + -6) = 0

Reorder the terms:
(3 + 2X)(-6 + 2X) = 0

Multiply (3 + 2X) * (-6 + 2X)
(3(-6 + 2X) + 2X * (-6 + 2X)) = 0
((-6 * 3 + 2X * 3) + 2X * (-6 + 2X)) = 0
((-18 + 6X) + 2X * (-6 + 2X)) = 0
(-18 + 6X + (-6 * 2X + 2X * 2X)) = 0
(-18 + 6X + (-12X + 4X2)) = 0

Combine like terms: 6X + -12X = -6X
(-18 + -6X + 4X2) = 0

Solving
-18 + -6X + 4X2 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + -3X + 2X2) = 0

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

Ignore the factor 2.

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

Simplifying
-3 + -2X = 0

Solving
-3 + -2X = 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 + -2X = 0 + 3

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

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

Divide each side by '-2'.
X = -1.5

Simplifying
X = -1.5

Subproblem 2
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
Solution
X = {-1.5, 3}

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