(2x-7)(5-3x)=0

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Solution for (2x-7)(5-3x)=0 equation: 


Simplifying
(2x + -7)(5 + -3x) = 0

Reorder the terms:
(-7 + 2x)(5 + -3x) = 0

Multiply (-7 + 2x) * (5 + -3x)
(-7(5 + -3x) + 2x * (5 + -3x)) = 0
((5 * -7 + -3x * -7) + 2x * (5 + -3x)) = 0
((-35 + 21x) + 2x * (5 + -3x)) = 0
(-35 + 21x + (5 * 2x + -3x * 2x)) = 0
(-35 + 21x + (10x + -6x2)) = 0

Combine like terms: 21x + 10x = 31x
(-35 + 31x + -6x2) = 0

Solving
-35 + 31x + -6x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-7 + 2x)(5 + -3x) = 0


Subproblem 1
Set the factor '(-7 + 2x)' equal to zero and attempt to solve:

Simplifying
-7 + 2x = 0

Solving
-7 + 2x = 0

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

Add '7' to each side of the equation.
-7 + 7 + 2x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 2x = 0 + 7
2x = 0 + 7

Combine like terms: 0 + 7 = 7
2x = 7

Divide each side by '2'.
x = 3.5

Simplifying
x = 3.5

Subproblem 2
Set the factor '(5 + -3x)' equal to zero and attempt to solve:

Simplifying
5 + -3x = 0

Solving
5 + -3x = 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 + -3x = 0 + -5

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

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

Divide each side by '-3'.
x = 1.666666667

Simplifying
x = 1.666666667
Solution
x = {3.5, 1.666666667}

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