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

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


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

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

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

Multiply (2 + x) * (-7 + 2x)
6(2(-7 + 2x) + x(-7 + 2x)) = 0
6((-7 * 2 + 2x * 2) + x(-7 + 2x)) = 0
6((-14 + 4x) + x(-7 + 2x)) = 0
6(-14 + 4x + (-7 * x + 2x * x)) = 0
6(-14 + 4x + (-7x + 2x2)) = 0

Combine like terms: 4x + -7x = -3x
6(-14 + -3x + 2x2) = 0
(-14 * 6 + -3x * 6 + 2x2 * 6) = 0
(-84 + -18x + 12x2) = 0

Solving
-84 + -18x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-14 + -3x + 2x2) = 0

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

Ignore the factor 6.

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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

Subproblem 2
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
Solution
x = {-2, 3.5}

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