-2(2X+3)(X-5)=0

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Solution for -2(2X+3)(X-5)=0 equation: 


Simplifying
-2(2X + 3)(X + -5) = 0

Reorder the terms:
-2(3 + 2X)(X + -5) = 0

Reorder the terms:
-2(3 + 2X)(-5 + X) = 0

Multiply (3 + 2X) * (-5 + X)
-2(3(-5 + X) + 2X * (-5 + X)) = 0
-2((-5 * 3 + X * 3) + 2X * (-5 + X)) = 0
-2((-15 + 3X) + 2X * (-5 + X)) = 0
-2(-15 + 3X + (-5 * 2X + X * 2X)) = 0
-2(-15 + 3X + (-10X + 2X2)) = 0

Combine like terms: 3X + -10X = -7X
-2(-15 + -7X + 2X2) = 0
(-15 * -2 + -7X * -2 + 2X2 * -2) = 0
(30 + 14X + -4X2) = 0

Solving
30 + 14X + -4X2 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '2'.
2(15 + 7X + -2X2) = 0

Factor a trinomial.
2((5 + -1X)(3 + 2X)) = 0

Ignore the factor 2.

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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