2(2x-5)(6x+11)=0

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Solution for 2(2x-5)(6x+11)=0 equation: 


Simplifying
2(2x + -5)(6x + 11) = 0

Reorder the terms:
2(-5 + 2x)(6x + 11) = 0

Reorder the terms:
2(-5 + 2x)(11 + 6x) = 0

Multiply (-5 + 2x) * (11 + 6x)
2(-5(11 + 6x) + 2x * (11 + 6x)) = 0
2((11 * -5 + 6x * -5) + 2x * (11 + 6x)) = 0
2((-55 + -30x) + 2x * (11 + 6x)) = 0
2(-55 + -30x + (11 * 2x + 6x * 2x)) = 0
2(-55 + -30x + (22x + 12x2)) = 0

Combine like terms: -30x + 22x = -8x
2(-55 + -8x + 12x2) = 0
(-55 * 2 + -8x * 2 + 12x2 * 2) = 0
(-110 + -16x + 24x2) = 0

Solving
-110 + -16x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-55 + -8x + 12x2) = 0

Factor a trinomial.
2((-11 + -6x)(5 + -2x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-11 + -6x)' equal to zero and attempt to solve:

Simplifying
-11 + -6x = 0

Solving
-11 + -6x = 0

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

Add '11' to each side of the equation.
-11 + 11 + -6x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -6x = 0 + 11
-6x = 0 + 11

Combine like terms: 0 + 11 = 11
-6x = 11

Divide each side by '-6'.
x = -1.833333333

Simplifying
x = -1.833333333

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 = {-1.833333333, 2.5}

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