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

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


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

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

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

Combine like terms: 3x + 28x = 31x
(-21 + 31x + -4x2) = 0

Solving
-21 + 31x + -4x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-7 + x)(3 + -4x) = 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 '(3 + -4x)' equal to zero and attempt to solve:

Simplifying
3 + -4x = 0

Solving
3 + -4x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -4x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4x = 0 + -3
-4x = 0 + -3

Combine like terms: 0 + -3 = -3
-4x = -3

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75
Solution
x = {7, 0.75}

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