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

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


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

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

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

Combine like terms: 15x + 8x = 23x
(-20 + 23x + -6x2) = 0

Solving
-20 + 23x + -6x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-5 + 2x)(4 + -3x) = 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 '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

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

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

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

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333
Solution
x = {2.5, 1.333333333}

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