6(2x+7)(x-4)=0

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Solution for 6(2x+7)(x-4)=0 equation: 


Simplifying
6(2x + 7)(x + -4) = 0

Reorder the terms:
6(7 + 2x)(x + -4) = 0

Reorder the terms:
6(7 + 2x)(-4 + x) = 0

Multiply (7 + 2x) * (-4 + x)
6(7(-4 + x) + 2x * (-4 + x)) = 0
6((-4 * 7 + x * 7) + 2x * (-4 + x)) = 0
6((-28 + 7x) + 2x * (-4 + x)) = 0
6(-28 + 7x + (-4 * 2x + x * 2x)) = 0
6(-28 + 7x + (-8x + 2x2)) = 0

Combine like terms: 7x + -8x = -1x
6(-28 + -1x + 2x2) = 0
(-28 * 6 + -1x * 6 + 2x2 * 6) = 0
(-168 + -6x + 12x2) = 0

Solving
-168 + -6x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-28 + -1x + 2x2) = 0

Factor a trinomial.
6((-7 + -2x)(4 + -1x)) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-7 + -2x)' equal to zero and attempt to solve:

Simplifying
-7 + -2x = 0

Solving
-7 + -2x = 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 + -2x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2x = 0 + 7
-2x = 0 + 7

Combine like terms: 0 + 7 = 7
-2x = 7

Divide each side by '-2'.
x = -3.5

Simplifying
x = -3.5

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-3.5, 4}

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