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

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


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

Reorder the terms:
(-3 + 6x)(3x + 15) = 0

Reorder the terms:
(-3 + 6x)(15 + 3x) = 0

Multiply (-3 + 6x) * (15 + 3x)
(-3(15 + 3x) + 6x * (15 + 3x)) = 0
((15 * -3 + 3x * -3) + 6x * (15 + 3x)) = 0
((-45 + -9x) + 6x * (15 + 3x)) = 0
(-45 + -9x + (15 * 6x + 3x * 6x)) = 0
(-45 + -9x + (90x + 18x2)) = 0

Combine like terms: -9x + 90x = 81x
(-45 + 81x + 18x2) = 0

Solving
-45 + 81x + 18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '9'.
9(-5 + 9x + 2x2) = 0

Factor a trinomial.
9((-5 + -1x)(1 + -2x)) = 0

Ignore the factor 9.

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

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 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 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5

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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

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

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

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

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

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {-5, 0.5}

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