(-6x+9)(-3x-15)=0

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Solution for (-6x+9)(-3x-15)=0 equation: 


Simplifying
(-6x + 9)(-3x + -15) = 0

Reorder the terms:
(9 + -6x)(-3x + -15) = 0

Reorder the terms:
(9 + -6x)(-15 + -3x) = 0

Multiply (9 + -6x) * (-15 + -3x)
(9(-15 + -3x) + -6x * (-15 + -3x)) = 0
((-15 * 9 + -3x * 9) + -6x * (-15 + -3x)) = 0
((-135 + -27x) + -6x * (-15 + -3x)) = 0
(-135 + -27x + (-15 * -6x + -3x * -6x)) = 0
(-135 + -27x + (90x + 18x2)) = 0

Combine like terms: -27x + 90x = 63x
(-135 + 63x + 18x2) = 0

Solving
-135 + 63x + 18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '9'.
9(-15 + 7x + 2x2) = 0

Factor a trinomial.
9((-5 + -1x)(3 + -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 '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-5, 1.5}

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