(4x+3)(5-2x)=0

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Solution for (4x+3)(5-2x)=0 equation: 


Simplifying
(4x + 3)(5 + -2x) = 0

Reorder the terms:
(3 + 4x)(5 + -2x) = 0

Multiply (3 + 4x) * (5 + -2x)
(3(5 + -2x) + 4x * (5 + -2x)) = 0
((5 * 3 + -2x * 3) + 4x * (5 + -2x)) = 0
((15 + -6x) + 4x * (5 + -2x)) = 0
(15 + -6x + (5 * 4x + -2x * 4x)) = 0
(15 + -6x + (20x + -8x2)) = 0

Combine like terms: -6x + 20x = 14x
(15 + 14x + -8x2) = 0

Solving
15 + 14x + -8x2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

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 = {2.5, -0.75}

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