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

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


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

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

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

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

Combine like terms: 35x + -24x = 11x
(-40 + 11x + 21x2) = 0

Solving
-40 + 11x + 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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