3(6x-5)(4x+7)=0

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Solution for 3(6x-5)(4x+7)=0 equation: 


Simplifying
3(6x + -5)(4x + 7) = 0

Reorder the terms:
3(-5 + 6x)(4x + 7) = 0

Reorder the terms:
3(-5 + 6x)(7 + 4x) = 0

Multiply (-5 + 6x) * (7 + 4x)
3(-5(7 + 4x) + 6x * (7 + 4x)) = 0
3((7 * -5 + 4x * -5) + 6x * (7 + 4x)) = 0
3((-35 + -20x) + 6x * (7 + 4x)) = 0
3(-35 + -20x + (7 * 6x + 4x * 6x)) = 0
3(-35 + -20x + (42x + 24x2)) = 0

Combine like terms: -20x + 42x = 22x
3(-35 + 22x + 24x2) = 0
(-35 * 3 + 22x * 3 + 24x2 * 3) = 0
(-105 + 66x + 72x2) = 0

Solving
-105 + 66x + 72x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-35 + 22x + 24x2) = 0

Factor a trinomial.
3((-7 + -4x)(5 + -6x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-7 + -4x)' equal to zero and attempt to solve:

Simplifying
-7 + -4x = 0

Solving
-7 + -4x = 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 + -4x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -4x = 0 + 7
-4x = 0 + 7

Combine like terms: 0 + 7 = 7
-4x = 7

Divide each side by '-4'.
x = -1.75

Simplifying
x = -1.75

Subproblem 2
Set the factor '(5 + -6x)' equal to zero and attempt to solve:

Simplifying
5 + -6x = 0

Solving
5 + -6x = 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 + -6x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -6x = 0 + -5
-6x = 0 + -5

Combine like terms: 0 + -5 = -5
-6x = -5

Divide each side by '-6'.
x = 0.8333333333

Simplifying
x = 0.8333333333
Solution
x = {-1.75, 0.8333333333}

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