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

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


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

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

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

Multiply (-5 + 2x) * (3 + x)
2(-5(3 + x) + 2x * (3 + x)) = 0
2((3 * -5 + x * -5) + 2x * (3 + x)) = 0
2((-15 + -5x) + 2x * (3 + x)) = 0
2(-15 + -5x + (3 * 2x + x * 2x)) = 0
2(-15 + -5x + (6x + 2x2)) = 0

Combine like terms: -5x + 6x = 1x
2(-15 + 1x + 2x2) = 0
(-15 * 2 + 1x * 2 + 2x2 * 2) = 0
(-30 + 2x + 4x2) = 0

Solving
-30 + 2x + 4x2 = 0

Solving for variable 'x'.

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

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

Ignore the factor 2.

Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 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 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

Subproblem 2
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
Solution
x = {-3, 2.5}

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