3(3x-4)(6x+7)=0

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Solution for 3(3x-4)(6x+7)=0 equation: 


Simplifying
3(3x + -4)(6x + 7) = 0

Reorder the terms:
3(-4 + 3x)(6x + 7) = 0

Reorder the terms:
3(-4 + 3x)(7 + 6x) = 0

Multiply (-4 + 3x) * (7 + 6x)
3(-4(7 + 6x) + 3x * (7 + 6x)) = 0
3((7 * -4 + 6x * -4) + 3x * (7 + 6x)) = 0
3((-28 + -24x) + 3x * (7 + 6x)) = 0
3(-28 + -24x + (7 * 3x + 6x * 3x)) = 0
3(-28 + -24x + (21x + 18x2)) = 0

Combine like terms: -24x + 21x = -3x
3(-28 + -3x + 18x2) = 0
(-28 * 3 + -3x * 3 + 18x2 * 3) = 0
(-84 + -9x + 54x2) = 0

Solving
-84 + -9x + 54x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-28 + -3x + 18x2) = 0

Factor a trinomial.
3((-7 + -6x)(4 + -3x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-7 + -6x)' equal to zero and attempt to solve:

Simplifying
-7 + -6x = 0

Solving
-7 + -6x = 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 + -6x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -6x = 0 + 7
-6x = 0 + 7

Combine like terms: 0 + 7 = 7
-6x = 7

Divide each side by '-6'.
x = -1.166666667

Simplifying
x = -1.166666667

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 = {-1.166666667, 1.333333333}

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