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

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


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

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

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

Multiply (8 + -7x) * (-8 + 3x)
(8(-8 + 3x) + -7x * (-8 + 3x)) = 0
((-8 * 8 + 3x * 8) + -7x * (-8 + 3x)) = 0
((-64 + 24x) + -7x * (-8 + 3x)) = 0
(-64 + 24x + (-8 * -7x + 3x * -7x)) = 0
(-64 + 24x + (56x + -21x2)) = 0

Combine like terms: 24x + 56x = 80x
(-64 + 80x + -21x2) = 0

Solving
-64 + 80x + -21x2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(-8 + 3x)' equal to zero and attempt to solve:

Simplifying
-8 + 3x = 0

Solving
-8 + 3x = 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 + 3x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 3x = 0 + 8
3x = 0 + 8

Combine like terms: 0 + 8 = 8
3x = 8

Divide each side by '3'.
x = 2.666666667

Simplifying
x = 2.666666667

Subproblem 2
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
Solution
x = {2.666666667, 1.142857143}

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