37(4-1x)(5+3x)=0

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Solution for 37(4-1x)(5+3x)=0 equation: 


Simplifying
37(4 + -1x)(5 + 3x) = 0

Multiply (4 + -1x) * (5 + 3x)
37(4(5 + 3x) + -1x * (5 + 3x)) = 0
37((5 * 4 + 3x * 4) + -1x * (5 + 3x)) = 0
37((20 + 12x) + -1x * (5 + 3x)) = 0
37(20 + 12x + (5 * -1x + 3x * -1x)) = 0
37(20 + 12x + (-5x + -3x2)) = 0

Combine like terms: 12x + -5x = 7x
37(20 + 7x + -3x2) = 0
(20 * 37 + 7x * 37 + -3x2 * 37) = 0
(740 + 259x + -111x2) = 0

Solving
740 + 259x + -111x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '37'.
37(20 + 7x + -3x2) = 0

Factor a trinomial.
37((4 + -1x)(5 + 3x)) = 0

Ignore the factor 37.

Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

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 = {4, -1.666666667}

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