(3x-2)(12x+7)=0

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Solution for (3x-2)(12x+7)=0 equation: 


Simplifying
(3x + -2)(12x + 7) = 0

Reorder the terms:
(-2 + 3x)(12x + 7) = 0

Reorder the terms:
(-2 + 3x)(7 + 12x) = 0

Multiply (-2 + 3x) * (7 + 12x)
(-2(7 + 12x) + 3x * (7 + 12x)) = 0
((7 * -2 + 12x * -2) + 3x * (7 + 12x)) = 0
((-14 + -24x) + 3x * (7 + 12x)) = 0
(-14 + -24x + (7 * 3x + 12x * 3x)) = 0
(-14 + -24x + (21x + 36x2)) = 0

Combine like terms: -24x + 21x = -3x
(-14 + -3x + 36x2) = 0

Solving
-14 + -3x + 36x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-7 + -12x)(2 + -3x) = 0


Subproblem 1
Set the factor '(-7 + -12x)' equal to zero and attempt to solve:

Simplifying
-7 + -12x = 0

Solving
-7 + -12x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -12x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -12x = 0 + 7
-12x = 0 + 7

Combine like terms: 0 + 7 = 7
-12x = 7

Divide each side by '-12'.
x = -0.5833333333

Simplifying
x = -0.5833333333

Subproblem 2
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
Solution
x = {-0.5833333333, 0.6666666667}

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