(2x-9)(7-x)=0

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Solution for (2x-9)(7-x)=0 equation: 


Simplifying
(2x + -9)(7 + -1x) = 0

Reorder the terms:
(-9 + 2x)(7 + -1x) = 0

Multiply (-9 + 2x) * (7 + -1x)
(-9(7 + -1x) + 2x * (7 + -1x)) = 0
((7 * -9 + -1x * -9) + 2x * (7 + -1x)) = 0
((-63 + 9x) + 2x * (7 + -1x)) = 0
(-63 + 9x + (7 * 2x + -1x * 2x)) = 0
(-63 + 9x + (14x + -2x2)) = 0

Combine like terms: 9x + 14x = 23x
(-63 + 23x + -2x2) = 0

Solving
-63 + 23x + -2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-7 + x)(9 + -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 '(9 + -2x)' equal to zero and attempt to solve:

Simplifying
9 + -2x = 0

Solving
9 + -2x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -2x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2x = 0 + -9
-2x = 0 + -9

Combine like terms: 0 + -9 = -9
-2x = -9

Divide each side by '-2'.
x = 4.5

Simplifying
x = 4.5
Solution
x = {7, 4.5}

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