(-7x+8)(3x-5)=0

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Solution for (-7x+8)(3x-5)=0 equation: 


Simplifying
(-7x + 8)(3x + -5) = 0

Reorder the terms:
(8 + -7x)(3x + -5) = 0

Reorder the terms:
(8 + -7x)(-5 + 3x) = 0

Multiply (8 + -7x) * (-5 + 3x)
(8(-5 + 3x) + -7x * (-5 + 3x)) = 0
((-5 * 8 + 3x * 8) + -7x * (-5 + 3x)) = 0
((-40 + 24x) + -7x * (-5 + 3x)) = 0
(-40 + 24x + (-5 * -7x + 3x * -7x)) = 0
(-40 + 24x + (35x + -21x2)) = 0

Combine like terms: 24x + 35x = 59x
(-40 + 59x + -21x2) = 0

Solving
-40 + 59x + -21x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-5 + 3x)(8 + -7x) = 0


Subproblem 1
Set the factor '(-5 + 3x)' equal to zero and attempt to solve:

Simplifying
-5 + 3x = 0

Solving
-5 + 3x = 0

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

Add '5' to each side of the equation.
-5 + 5 + 3x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 3x = 0 + 5
3x = 0 + 5

Combine like terms: 0 + 5 = 5
3x = 5

Divide each side by '3'.
x = 1.666666667

Simplifying
x = 1.666666667

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 = {1.666666667, 1.142857143}

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