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

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


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

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

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

Multiply (-7 + 4x) * (4 + 5x)
6(-7(4 + 5x) + 4x * (4 + 5x)) = 0
6((4 * -7 + 5x * -7) + 4x * (4 + 5x)) = 0
6((-28 + -35x) + 4x * (4 + 5x)) = 0
6(-28 + -35x + (4 * 4x + 5x * 4x)) = 0
6(-28 + -35x + (16x + 20x2)) = 0

Combine like terms: -35x + 16x = -19x
6(-28 + -19x + 20x2) = 0
(-28 * 6 + -19x * 6 + 20x2 * 6) = 0
(-168 + -114x + 120x2) = 0

Solving
-168 + -114x + 120x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-28 + -19x + 20x2) = 0

Factor a trinomial.
6((-4 + -5x)(7 + -4x)) = 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 + -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
Solution
x = {-0.8, 1.75}

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