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

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


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

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

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

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

Combine like terms: -56x + 15x = -41x
(-24 + -41x + 35x2) = 0

Solving
-24 + -41x + 35x2 = 0

Solving for variable 'x'.

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


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

Simplifying
-3 + -7x = 0

Solving
-3 + -7x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -7x = 0 + 3

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

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

Divide each side by '-7'.
x = -0.4285714286

Simplifying
x = -0.4285714286

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 = {-0.4285714286, 1.6}

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