(5x+2)*(16-8x)=0

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Solution for (5x+2)*(16-8x)=0 equation: 


Simplifying
(5x + 2)(16 + -8x) = 0

Reorder the terms:
(2 + 5x)(16 + -8x) = 0

Multiply (2 + 5x) * (16 + -8x)
(2(16 + -8x) + 5x * (16 + -8x)) = 0
((16 * 2 + -8x * 2) + 5x * (16 + -8x)) = 0
((32 + -16x) + 5x * (16 + -8x)) = 0
(32 + -16x + (16 * 5x + -8x * 5x)) = 0
(32 + -16x + (80x + -40x2)) = 0

Combine like terms: -16x + 80x = 64x
(32 + 64x + -40x2) = 0

Solving
32 + 64x + -40x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8'.
8(4 + 8x + -5x2) = 0

Factor a trinomial.
8((2 + -1x)(2 + 5x)) = 0

Ignore the factor 8.

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 '(2 + 5x)' equal to zero and attempt to solve:

Simplifying
2 + 5x = 0

Solving
2 + 5x = 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 + 5x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5x = 0 + -2
5x = 0 + -2

Combine like terms: 0 + -2 = -2
5x = -2

Divide each side by '5'.
x = -0.4

Simplifying
x = -0.4
Solution
x = {2, -0.4}

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