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

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


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

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

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

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

Combine like terms: -35x + 18x = -17x
3(-21 + -17x + 30x2) = 0
(-21 * 3 + -17x * 3 + 30x2 * 3) = 0
(-63 + -51x + 90x2) = 0

Solving
-63 + -51x + 90x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-21 + -17x + 30x2) = 0

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

Ignore the factor 3.

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

Simplifying
-3 + -5x = 0

Solving
-3 + -5x = 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 + -5x = 0 + 3

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

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

Divide each side by '-5'.
x = -0.6

Simplifying
x = -0.6

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 = {-0.6, 1.166666667}

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