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

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


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

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

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

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

Solving
24 + 17x + -20x2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

Subproblem 2
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
Solution
x = {1.6, -0.75}

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