(5x+8)(3-4x)=0

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Solution for (5x+8)(3-4x)=0 equation: 


Simplifying
(5x + 8)(3 + -4x) = 0

Reorder the terms:
(8 + 5x)(3 + -4x) = 0

Multiply (8 + 5x) * (3 + -4x)
(8(3 + -4x) + 5x * (3 + -4x)) = 0
((3 * 8 + -4x * 8) + 5x * (3 + -4x)) = 0
((24 + -32x) + 5x * (3 + -4x)) = 0
(24 + -32x + (3 * 5x + -4x * 5x)) = 0
(24 + -32x + (15x + -20x2)) = 0

Combine like terms: -32x + 15x = -17x
(24 + -17x + -20x2) = 0

Solving
24 + -17x + -20x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3 + -4x)(8 + 5x) = 0


Subproblem 1
Set the factor '(3 + -4x)' equal to zero and attempt to solve:

Simplifying
3 + -4x = 0

Solving
3 + -4x = 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 + -4x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4x = 0 + -3
-4x = 0 + -3

Combine like terms: 0 + -3 = -3
-4x = -3

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75

Subproblem 2
Set the factor '(8 + 5x)' equal to zero and attempt to solve:

Simplifying
8 + 5x = 0

Solving
8 + 5x = 0

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

Add '-8' to each side of the equation.
8 + -8 + 5x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 5x = 0 + -8
5x = 0 + -8

Combine like terms: 0 + -8 = -8
5x = -8

Divide each side by '5'.
x = -1.6

Simplifying
x = -1.6
Solution
x = {0.75, -1.6}

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