(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 = -11x
(-40 + -11x + 21x2) = 0

Solving
-40 + -11x + 21x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-8 + -7x)(5 + -3x) = 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 '(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
Solution
x = {-1.142857143, 1.666666667}

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