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

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


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

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

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

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

Combine like terms: -14x + 112x = 98x
(-56 + 98x + 28x2) = 0

Solving
-56 + 98x + 28x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '14'.
14(-4 + 7x + 2x2) = 0

Factor a trinomial.
14((-4 + -1x)(1 + -2x)) = 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 '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

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

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

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

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

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {-4, 0.5}

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