3(6x-7)(3x+5)=0

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Solution for 3(6x-7)(3x+5)=0 equation: 


Simplifying
3(6x + -7)(3x + 5) = 0

Reorder the terms:
3(-7 + 6x)(3x + 5) = 0

Reorder the terms:
3(-7 + 6x)(5 + 3x) = 0

Multiply (-7 + 6x) * (5 + 3x)
3(-7(5 + 3x) + 6x * (5 + 3x)) = 0
3((5 * -7 + 3x * -7) + 6x * (5 + 3x)) = 0
3((-35 + -21x) + 6x * (5 + 3x)) = 0
3(-35 + -21x + (5 * 6x + 3x * 6x)) = 0
3(-35 + -21x + (30x + 18x2)) = 0

Combine like terms: -21x + 30x = 9x
3(-35 + 9x + 18x2) = 0
(-35 * 3 + 9x * 3 + 18x2 * 3) = 0
(-105 + 27x + 54x2) = 0

Solving
-105 + 27x + 54x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-35 + 9x + 18x2) = 0

Factor a trinomial.
3((-5 + -3x)(7 + -6x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-5 + -3x)' equal to zero and attempt to solve:

Simplifying
-5 + -3x = 0

Solving
-5 + -3x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -3x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3x = 0 + 5
-3x = 0 + 5

Combine like terms: 0 + 5 = 5
-3x = 5

Divide each side by '-3'.
x = -1.666666667

Simplifying
x = -1.666666667

Subproblem 2
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
Solution
x = {-1.666666667, 1.166666667}

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