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

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


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

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

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

Multiply (-3 + x) * (-8 + 7x)
(-3(-8 + 7x) + x(-8 + 7x)) = 0
((-8 * -3 + 7x * -3) + x(-8 + 7x)) = 0
((24 + -21x) + x(-8 + 7x)) = 0
(24 + -21x + (-8 * x + 7x * x)) = 0
(24 + -21x + (-8x + 7x2)) = 0

Combine like terms: -21x + -8x = -29x
(24 + -29x + 7x2) = 0

Solving
24 + -29x + 7x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(8 + -7x)(3 + -1x) = 0


Subproblem 1
Set the factor '(8 + -7x)' equal to zero and attempt to solve:

Simplifying
8 + -7x = 0

Solving
8 + -7x = 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 + -7x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -7x = 0 + -8
-7x = 0 + -8

Combine like terms: 0 + -8 = -8
-7x = -8

Divide each side by '-7'.
x = 1.142857143

Simplifying
x = 1.142857143

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {1.142857143, 3}

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