(9*4+6*3+7x)(6*5+10*3+2x)=0

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Solution for (9*4+6*3+7x)(6*5+10*3+2x)=0 equation: 


Simplifying
(9 * 4 + 6 * 3 + 7x)(6 * 5 + 10 * 3 + 2x) = 0

Multiply 9 * 4
(36 + 6 * 3 + 7x)(6 * 5 + 10 * 3 + 2x) = 0

Multiply 6 * 3
(36 + 18 + 7x)(6 * 5 + 10 * 3 + 2x) = 0

Combine like terms: 36 + 18 = 54
(54 + 7x)(6 * 5 + 10 * 3 + 2x) = 0

Multiply 6 * 5
(54 + 7x)(30 + 10 * 3 + 2x) = 0

Multiply 10 * 3
(54 + 7x)(30 + 30 + 2x) = 0

Combine like terms: 30 + 30 = 60
(54 + 7x)(60 + 2x) = 0

Multiply (54 + 7x) * (60 + 2x)
(54(60 + 2x) + 7x * (60 + 2x)) = 0
((60 * 54 + 2x * 54) + 7x * (60 + 2x)) = 0
((3240 + 108x) + 7x * (60 + 2x)) = 0
(3240 + 108x + (60 * 7x + 2x * 7x)) = 0
(3240 + 108x + (420x + 14x2)) = 0

Combine like terms: 108x + 420x = 528x
(3240 + 528x + 14x2) = 0

Solving
3240 + 528x + 14x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1620 + 264x + 7x2) = 0

Factor a trinomial.
2((30 + x)(54 + 7x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(30 + x)' equal to zero and attempt to solve:

Simplifying
30 + x = 0

Solving
30 + x = 0

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

Add '-30' to each side of the equation.
30 + -30 + x = 0 + -30

Combine like terms: 30 + -30 = 0
0 + x = 0 + -30
x = 0 + -30

Combine like terms: 0 + -30 = -30
x = -30

Simplifying
x = -30

Subproblem 2
Set the factor '(54 + 7x)' equal to zero and attempt to solve:

Simplifying
54 + 7x = 0

Solving
54 + 7x = 0

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

Add '-54' to each side of the equation.
54 + -54 + 7x = 0 + -54

Combine like terms: 54 + -54 = 0
0 + 7x = 0 + -54
7x = 0 + -54

Combine like terms: 0 + -54 = -54
7x = -54

Divide each side by '7'.
x = -7.714285714

Simplifying
x = -7.714285714
Solution
x = {-30, -7.714285714}

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