(2x+6)(3x-4)=0

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Solution for (2x+6)(3x-4)=0 equation: 


Simplifying
(2x + 6)(3x + -4) = 0

Reorder the terms:
(6 + 2x)(3x + -4) = 0

Reorder the terms:
(6 + 2x)(-4 + 3x) = 0

Multiply (6 + 2x) * (-4 + 3x)
(6(-4 + 3x) + 2x * (-4 + 3x)) = 0
((-4 * 6 + 3x * 6) + 2x * (-4 + 3x)) = 0
((-24 + 18x) + 2x * (-4 + 3x)) = 0
(-24 + 18x + (-4 * 2x + 3x * 2x)) = 0
(-24 + 18x + (-8x + 6x2)) = 0

Combine like terms: 18x + -8x = 10x
(-24 + 10x + 6x2) = 0

Solving
-24 + 10x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + 5x + 3x2) = 0

Factor a trinomial.
2((-3 + -1x)(4 + -3x)) = 0

Ignore the factor 2.

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 '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333
Solution
x = {-3, 1.333333333}

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