(7x+14)(8-2x)=0

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Solution for (7x+14)(8-2x)=0 equation: 


Simplifying
(7x + 14)(8 + -2x) = 0

Reorder the terms:
(14 + 7x)(8 + -2x) = 0

Multiply (14 + 7x) * (8 + -2x)
(14(8 + -2x) + 7x * (8 + -2x)) = 0
((8 * 14 + -2x * 14) + 7x * (8 + -2x)) = 0
((112 + -28x) + 7x * (8 + -2x)) = 0
(112 + -28x + (8 * 7x + -2x * 7x)) = 0
(112 + -28x + (56x + -14x2)) = 0

Combine like terms: -28x + 56x = 28x
(112 + 28x + -14x2) = 0

Solving
112 + 28x + -14x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '14'.
14(8 + 2x + -1x2) = 0

Factor a trinomial.
14((4 + -1x)(2 + x)) = 0

Ignore the factor 14.

Subproblem 1
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

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

Simplifying
2 + x = 0

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

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

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

Simplifying
x = -2
Solution
x = {4, -2}

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