(3x-4)(7-x)=0

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Solution for (3x-4)(7-x)=0 equation: 


Simplifying
(3x + -4)(7 + -1x) = 0

Reorder the terms:
(-4 + 3x)(7 + -1x) = 0

Multiply (-4 + 3x) * (7 + -1x)
(-4(7 + -1x) + 3x * (7 + -1x)) = 0
((7 * -4 + -1x * -4) + 3x * (7 + -1x)) = 0
((-28 + 4x) + 3x * (7 + -1x)) = 0
(-28 + 4x + (7 * 3x + -1x * 3x)) = 0
(-28 + 4x + (21x + -3x2)) = 0

Combine like terms: 4x + 21x = 25x
(-28 + 25x + -3x2) = 0

Solving
-28 + 25x + -3x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-7 + x)(4 + -3x) = 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 '(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 = {7, 1.333333333}

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