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

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


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

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

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

Multiply (7 + -3x) * (-8 + 5x)
(7(-8 + 5x) + -3x * (-8 + 5x)) = 0
((-8 * 7 + 5x * 7) + -3x * (-8 + 5x)) = 0
((-56 + 35x) + -3x * (-8 + 5x)) = 0
(-56 + 35x + (-8 * -3x + 5x * -3x)) = 0
(-56 + 35x + (24x + -15x2)) = 0

Combine like terms: 35x + 24x = 59x
(-56 + 59x + -15x2) = 0

Solving
-56 + 59x + -15x2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(-7 + 3x)' equal to zero and attempt to solve:

Simplifying
-7 + 3x = 0

Solving
-7 + 3x = 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 + 3x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 3x = 0 + 7
3x = 0 + 7

Combine like terms: 0 + 7 = 7
3x = 7

Divide each side by '3'.
x = 2.333333333

Simplifying
x = 2.333333333

Subproblem 2
Set the factor '(8 + -5x)' equal to zero and attempt to solve:

Simplifying
8 + -5x = 0

Solving
8 + -5x = 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 + -5x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -5x = 0 + -8
-5x = 0 + -8

Combine like terms: 0 + -8 = -8
-5x = -8

Divide each side by '-5'.
x = 1.6

Simplifying
x = 1.6
Solution
x = {2.333333333, 1.6}

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