-4(2x-5)(3x+9)=0

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Solution for -4(2x-5)(3x+9)=0 equation: 


Simplifying
-4(2x + -5)(3x + 9) = 0

Reorder the terms:
-4(-5 + 2x)(3x + 9) = 0

Reorder the terms:
-4(-5 + 2x)(9 + 3x) = 0

Multiply (-5 + 2x) * (9 + 3x)
-4(-5(9 + 3x) + 2x * (9 + 3x)) = 0
-4((9 * -5 + 3x * -5) + 2x * (9 + 3x)) = 0
-4((-45 + -15x) + 2x * (9 + 3x)) = 0
-4(-45 + -15x + (9 * 2x + 3x * 2x)) = 0
-4(-45 + -15x + (18x + 6x2)) = 0

Combine like terms: -15x + 18x = 3x
-4(-45 + 3x + 6x2) = 0
(-45 * -4 + 3x * -4 + 6x2 * -4) = 0
(180 + -12x + -24x2) = 0

Solving
180 + -12x + -24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12'.
12(15 + -1x + -2x2) = 0

Factor a trinomial.
12((5 + -2x)(3 + x)) = 0

Ignore the factor 12.

Subproblem 1
Set the factor '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 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 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5

Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

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

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

Simplifying
x = -3
Solution
x = {2.5, -3}

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