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

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


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

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

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

Multiply (4 + 5x) * (-7 + 3x)
6(4(-7 + 3x) + 5x * (-7 + 3x)) = 0
6((-7 * 4 + 3x * 4) + 5x * (-7 + 3x)) = 0
6((-28 + 12x) + 5x * (-7 + 3x)) = 0
6(-28 + 12x + (-7 * 5x + 3x * 5x)) = 0
6(-28 + 12x + (-35x + 15x2)) = 0

Combine like terms: 12x + -35x = -23x
6(-28 + -23x + 15x2) = 0
(-28 * 6 + -23x * 6 + 15x2 * 6) = 0
(-168 + -138x + 90x2) = 0

Solving
-168 + -138x + 90x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-28 + -23x + 15x2) = 0

Factor a trinomial.
6((-4 + -5x)(7 + -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 '(7 + -3x)' equal to zero and attempt to solve:

Simplifying
7 + -3x = 0

Solving
7 + -3x = 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 + -3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3x = 0 + -7
-3x = 0 + -7

Combine like terms: 0 + -7 = -7
-3x = -7

Divide each side by '-3'.
x = 2.333333333

Simplifying
x = 2.333333333
Solution
x = {-0.8, 2.333333333}

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