(2x-8)(5x+3)=0

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Solution for (2x-8)(5x+3)=0 equation: 


Simplifying
(2x + -8)(5x + 3) = 0

Reorder the terms:
(-8 + 2x)(5x + 3) = 0

Reorder the terms:
(-8 + 2x)(3 + 5x) = 0

Multiply (-8 + 2x) * (3 + 5x)
(-8(3 + 5x) + 2x * (3 + 5x)) = 0
((3 * -8 + 5x * -8) + 2x * (3 + 5x)) = 0
((-24 + -40x) + 2x * (3 + 5x)) = 0
(-24 + -40x + (3 * 2x + 5x * 2x)) = 0
(-24 + -40x + (6x + 10x2)) = 0

Combine like terms: -40x + 6x = -34x
(-24 + -34x + 10x2) = 0

Solving
-24 + -34x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + -17x + 5x2) = 0

Factor a trinomial.
2((-3 + -5x)(4 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-3 + -5x)' equal to zero and attempt to solve:

Simplifying
-3 + -5x = 0

Solving
-3 + -5x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -5x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -5x = 0 + 3
-5x = 0 + 3

Combine like terms: 0 + 3 = 3
-5x = 3

Divide each side by '-5'.
x = -0.6

Simplifying
x = -0.6

Subproblem 2
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
Solution
x = {-0.6, 4}

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