(3x+7)(5-8x+32)=0

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Solution for (3x+7)(5-8x+32)=0 equation: 


Simplifying
(3x + 7)(5 + -8x + 32) = 0

Reorder the terms:
(7 + 3x)(5 + -8x + 32) = 0

Reorder the terms:
(7 + 3x)(5 + 32 + -8x) = 0

Combine like terms: 5 + 32 = 37
(7 + 3x)(37 + -8x) = 0

Multiply (7 + 3x) * (37 + -8x)
(7(37 + -8x) + 3x * (37 + -8x)) = 0
((37 * 7 + -8x * 7) + 3x * (37 + -8x)) = 0
((259 + -56x) + 3x * (37 + -8x)) = 0
(259 + -56x + (37 * 3x + -8x * 3x)) = 0
(259 + -56x + (111x + -24x2)) = 0

Combine like terms: -56x + 111x = 55x
(259 + 55x + -24x2) = 0

Solving
259 + 55x + -24x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(37 + -8x)(7 + 3x) = 0


Subproblem 1
Set the factor '(37 + -8x)' equal to zero and attempt to solve:

Simplifying
37 + -8x = 0

Solving
37 + -8x = 0

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

Add '-37' to each side of the equation.
37 + -37 + -8x = 0 + -37

Combine like terms: 37 + -37 = 0
0 + -8x = 0 + -37
-8x = 0 + -37

Combine like terms: 0 + -37 = -37
-8x = -37

Divide each side by '-8'.
x = 4.625

Simplifying
x = 4.625

Subproblem 2
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
Solution
x = {4.625, -2.333333333}

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