(6-3x)(15+7x)=0

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Solution for (6-3x)(15+7x)=0 equation: 


Simplifying
(6 + -3x)(15 + 7x) = 0

Multiply (6 + -3x) * (15 + 7x)
(6(15 + 7x) + -3x * (15 + 7x)) = 0
((15 * 6 + 7x * 6) + -3x * (15 + 7x)) = 0
((90 + 42x) + -3x * (15 + 7x)) = 0
(90 + 42x + (15 * -3x + 7x * -3x)) = 0
(90 + 42x + (-45x + -21x2)) = 0

Combine like terms: 42x + -45x = -3x
(90 + -3x + -21x2) = 0

Solving
90 + -3x + -21x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(30 + -1x + -7x2) = 0

Factor a trinomial.
3((2 + -1x)(15 + 7x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

Subproblem 2
Set the factor '(15 + 7x)' equal to zero and attempt to solve:

Simplifying
15 + 7x = 0

Solving
15 + 7x = 0

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

Add '-15' to each side of the equation.
15 + -15 + 7x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + 7x = 0 + -15
7x = 0 + -15

Combine like terms: 0 + -15 = -15
7x = -15

Divide each side by '7'.
x = -2.142857143

Simplifying
x = -2.142857143
Solution
x = {2, -2.142857143}

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