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

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


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

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

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

Multiply (2 + 3x) * (-6 + 4x)
(2(-6 + 4x) + 3x * (-6 + 4x)) = 0
((-6 * 2 + 4x * 2) + 3x * (-6 + 4x)) = 0
((-12 + 8x) + 3x * (-6 + 4x)) = 0
(-12 + 8x + (-6 * 3x + 4x * 3x)) = 0
(-12 + 8x + (-18x + 12x2)) = 0

Combine like terms: 8x + -18x = -10x
(-12 + -10x + 12x2) = 0

Solving
-12 + -10x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + -5x + 6x2) = 0

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

Ignore the factor 2.

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

Simplifying
-2 + -3x = 0

Solving
-2 + -3x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -3x = 0 + 2

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

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

Divide each side by '-3'.
x = -0.6666666667

Simplifying
x = -0.6666666667

Subproblem 2
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
Solution
x = {-0.6666666667, 1.5}

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