(6x+5)(3x-20-7)=0

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Solution for (6x+5)(3x-20-7)=0 equation: 


Simplifying
(6x + 5)(3x + -20 + -7) = 0

Reorder the terms:
(5 + 6x)(3x + -20 + -7) = 0

Reorder the terms:
(5 + 6x)(-20 + -7 + 3x) = 0

Combine like terms: -20 + -7 = -27
(5 + 6x)(-27 + 3x) = 0

Multiply (5 + 6x) * (-27 + 3x)
(5(-27 + 3x) + 6x * (-27 + 3x)) = 0
((-27 * 5 + 3x * 5) + 6x * (-27 + 3x)) = 0
((-135 + 15x) + 6x * (-27 + 3x)) = 0
(-135 + 15x + (-27 * 6x + 3x * 6x)) = 0
(-135 + 15x + (-162x + 18x2)) = 0

Combine like terms: 15x + -162x = -147x
(-135 + -147x + 18x2) = 0

Solving
-135 + -147x + 18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-45 + -49x + 6x2) = 0

Factor a trinomial.
3((-5 + -6x)(9 + -1x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-5 + -6x)' equal to zero and attempt to solve:

Simplifying
-5 + -6x = 0

Solving
-5 + -6x = 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 + -6x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -6x = 0 + 5
-6x = 0 + 5

Combine like terms: 0 + 5 = 5
-6x = 5

Divide each side by '-6'.
x = -0.8333333333

Simplifying
x = -0.8333333333

Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {-0.8333333333, 9}

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