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

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


Simplifying
(2x + 7) * 2(6 + -1x) * 2 = 0

Reorder the terms:
(7 + 2x) * 2(6 + -1x) * 2 = 0

Reorder the terms for easier multiplication:
2 * 2(7 + 2x)(6 + -1x) = 0

Multiply 2 * 2
4(7 + 2x)(6 + -1x) = 0

Multiply (7 + 2x) * (6 + -1x)
4(7(6 + -1x) + 2x * (6 + -1x)) = 0
4((6 * 7 + -1x * 7) + 2x * (6 + -1x)) = 0
4((42 + -7x) + 2x * (6 + -1x)) = 0
4(42 + -7x + (6 * 2x + -1x * 2x)) = 0
4(42 + -7x + (12x + -2x2)) = 0

Combine like terms: -7x + 12x = 5x
4(42 + 5x + -2x2) = 0
(42 * 4 + 5x * 4 + -2x2 * 4) = 0
(168 + 20x + -8x2) = 0

Solving
168 + 20x + -8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(42 + 5x + -2x2) = 0

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

Ignore the factor 4.

Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6

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 = {6, -3.5}

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