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

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


Simplifying
(2x + -5)(7 + -1x) = 0

Reorder the terms:
(-5 + 2x)(7 + -1x) = 0

Multiply (-5 + 2x) * (7 + -1x)
(-5(7 + -1x) + 2x * (7 + -1x)) = 0
((7 * -5 + -1x * -5) + 2x * (7 + -1x)) = 0
((-35 + 5x) + 2x * (7 + -1x)) = 0
(-35 + 5x + (7 * 2x + -1x * 2x)) = 0
(-35 + 5x + (14x + -2x2)) = 0

Combine like terms: 5x + 14x = 19x
(-35 + 19x + -2x2) = 0

Solving
-35 + 19x + -2x2 = 0

Solving for variable 'x'.

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


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

Simplifying
-7 + x = 0

Solving
-7 + x = 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 + x = 0 + 7

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

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

Simplifying
x = 7

Subproblem 2
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
Solution
x = {7, 2.5}

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