(2x+5)(3x-9)=-45

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Solution for (2x+5)(3x-9)=-45 equation: 


Simplifying
(2x + 5)(3x + -9) = -45

Reorder the terms:
(5 + 2x)(3x + -9) = -45

Reorder the terms:
(5 + 2x)(-9 + 3x) = -45

Multiply (5 + 2x) * (-9 + 3x)
(5(-9 + 3x) + 2x * (-9 + 3x)) = -45
((-9 * 5 + 3x * 5) + 2x * (-9 + 3x)) = -45
((-45 + 15x) + 2x * (-9 + 3x)) = -45
(-45 + 15x + (-9 * 2x + 3x * 2x)) = -45
(-45 + 15x + (-18x + 6x2)) = -45

Combine like terms: 15x + -18x = -3x
(-45 + -3x + 6x2) = -45

Add '45' to each side of the equation.
-45 + -3x + 45 + 6x2 = -45 + 45

Reorder the terms:
-45 + 45 + -3x + 6x2 = -45 + 45

Combine like terms: -45 + 45 = 0
0 + -3x + 6x2 = -45 + 45
-3x + 6x2 = -45 + 45

Combine like terms: -45 + 45 = 0
-3x + 6x2 = 0

Solving
-3x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-1 + 2x) = 0

Ignore the factor 3.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

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 = {0, 0.5}

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