3(6x-8)(7x+9)=0

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Solution for 3(6x-8)(7x+9)=0 equation: 


Simplifying
3(6x + -8)(7x + 9) = 0

Reorder the terms:
3(-8 + 6x)(7x + 9) = 0

Reorder the terms:
3(-8 + 6x)(9 + 7x) = 0

Multiply (-8 + 6x) * (9 + 7x)
3(-8(9 + 7x) + 6x * (9 + 7x)) = 0
3((9 * -8 + 7x * -8) + 6x * (9 + 7x)) = 0
3((-72 + -56x) + 6x * (9 + 7x)) = 0
3(-72 + -56x + (9 * 6x + 7x * 6x)) = 0
3(-72 + -56x + (54x + 42x2)) = 0

Combine like terms: -56x + 54x = -2x
3(-72 + -2x + 42x2) = 0
(-72 * 3 + -2x * 3 + 42x2 * 3) = 0
(-216 + -6x + 126x2) = 0

Solving
-216 + -6x + 126x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-36 + -1x + 21x2) = 0

Factor a trinomial.
6((-9 + -7x)(4 + -3x)) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-9 + -7x)' equal to zero and attempt to solve:

Simplifying
-9 + -7x = 0

Solving
-9 + -7x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -7x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -7x = 0 + 9
-7x = 0 + 9

Combine like terms: 0 + 9 = 9
-7x = 9

Divide each side by '-7'.
x = -1.285714286

Simplifying
x = -1.285714286

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 = {-1.285714286, 1.333333333}

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