(4x+8)(2x-5)=0

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Solution for (4x+8)(2x-5)=0 equation: 


Simplifying
(4x + 8)(2x + -5) = 0

Reorder the terms:
(8 + 4x)(2x + -5) = 0

Reorder the terms:
(8 + 4x)(-5 + 2x) = 0

Multiply (8 + 4x) * (-5 + 2x)
(8(-5 + 2x) + 4x * (-5 + 2x)) = 0
((-5 * 8 + 2x * 8) + 4x * (-5 + 2x)) = 0
((-40 + 16x) + 4x * (-5 + 2x)) = 0
(-40 + 16x + (-5 * 4x + 2x * 4x)) = 0
(-40 + 16x + (-20x + 8x2)) = 0

Combine like terms: 16x + -20x = -4x
(-40 + -4x + 8x2) = 0

Solving
-40 + -4x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-10 + -1x + 2x2) = 0

Factor a trinomial.
4((-2 + -1x)(5 + -2x)) = 0

Ignore the factor 4.

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

Simplifying
5 + -2x = 0

Solving
5 + -2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2x = 0 + -5

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

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

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {-2, 2.5}

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