6(5x+4)(3x-1)=0

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Solution for 6(5x+4)(3x-1)=0 equation: 


Simplifying
6(5x + 4)(3x + -1) = 0

Reorder the terms:
6(4 + 5x)(3x + -1) = 0

Reorder the terms:
6(4 + 5x)(-1 + 3x) = 0

Multiply (4 + 5x) * (-1 + 3x)
6(4(-1 + 3x) + 5x * (-1 + 3x)) = 0
6((-1 * 4 + 3x * 4) + 5x * (-1 + 3x)) = 0
6((-4 + 12x) + 5x * (-1 + 3x)) = 0
6(-4 + 12x + (-1 * 5x + 3x * 5x)) = 0
6(-4 + 12x + (-5x + 15x2)) = 0

Combine like terms: 12x + -5x = 7x
6(-4 + 7x + 15x2) = 0
(-4 * 6 + 7x * 6 + 15x2 * 6) = 0
(-24 + 42x + 90x2) = 0

Solving
-24 + 42x + 90x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-4 + 7x + 15x2) = 0

Factor a trinomial.
6((-4 + -5x)(1 + -3x)) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-4 + -5x)' equal to zero and attempt to solve:

Simplifying
-4 + -5x = 0

Solving
-4 + -5x = 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 + -5x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -5x = 0 + 4
-5x = 0 + 4

Combine like terms: 0 + 4 = 4
-5x = 4

Divide each side by '-5'.
x = -0.8

Simplifying
x = -0.8

Subproblem 2
Set the factor '(1 + -3x)' equal to zero and attempt to solve:

Simplifying
1 + -3x = 0

Solving
1 + -3x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3x = 0 + -1
-3x = 0 + -1

Combine like terms: 0 + -1 = -1
-3x = -1

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Solution
x = {-0.8, 0.3333333333}

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