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

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


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

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

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

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

Combine like terms: -16x + 35x = 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((-7 + -4x)(4 + -5x)) = 0

Ignore the factor 6.

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 '(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
Solution
x = {-1.75, 0.8}

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