(3x-7)(8-x)=0

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Solution for (3x-7)(8-x)=0 equation: 


Simplifying
(3x + -7)(8 + -1x) = 0

Reorder the terms:
(-7 + 3x)(8 + -1x) = 0

Multiply (-7 + 3x) * (8 + -1x)
(-7(8 + -1x) + 3x * (8 + -1x)) = 0
((8 * -7 + -1x * -7) + 3x * (8 + -1x)) = 0
((-56 + 7x) + 3x * (8 + -1x)) = 0
(-56 + 7x + (8 * 3x + -1x * 3x)) = 0
(-56 + 7x + (24x + -3x2)) = 0

Combine like terms: 7x + 24x = 31x
(-56 + 31x + -3x2) = 0

Solving
-56 + 31x + -3x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-8 + x)(7 + -3x) = 0


Subproblem 1
Set the factor '(-8 + x)' equal to zero and attempt to solve:

Simplifying
-8 + x = 0

Solving
-8 + x = 0

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

Add '8' to each side of the equation.
-8 + 8 + x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + x = 0 + 8
x = 0 + 8

Combine like terms: 0 + 8 = 8
x = 8

Simplifying
x = 8

Subproblem 2
Set the factor '(7 + -3x)' equal to zero and attempt to solve:

Simplifying
7 + -3x = 0

Solving
7 + -3x = 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 + -3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3x = 0 + -7
-3x = 0 + -7

Combine like terms: 0 + -7 = -7
-3x = -7

Divide each side by '-3'.
x = 2.333333333

Simplifying
x = 2.333333333
Solution
x = {8, 2.333333333}

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