(2x-5)(3x+2)=2(3x-11)

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Solution for (2x-5)(3x+2)=2(3x-11) equation: 


Simplifying
(2x + -5)(3x + 2) = 2(3x + -11)

Reorder the terms:
(-5 + 2x)(3x + 2) = 2(3x + -11)

Reorder the terms:
(-5 + 2x)(2 + 3x) = 2(3x + -11)

Multiply (-5 + 2x) * (2 + 3x)
(-5(2 + 3x) + 2x * (2 + 3x)) = 2(3x + -11)
((2 * -5 + 3x * -5) + 2x * (2 + 3x)) = 2(3x + -11)
((-10 + -15x) + 2x * (2 + 3x)) = 2(3x + -11)
(-10 + -15x + (2 * 2x + 3x * 2x)) = 2(3x + -11)
(-10 + -15x + (4x + 6x2)) = 2(3x + -11)

Combine like terms: -15x + 4x = -11x
(-10 + -11x + 6x2) = 2(3x + -11)

Reorder the terms:
-10 + -11x + 6x2 = 2(-11 + 3x)
-10 + -11x + 6x2 = (-11 * 2 + 3x * 2)
-10 + -11x + 6x2 = (-22 + 6x)

Solving
-10 + -11x + 6x2 = -22 + 6x

Solving for variable 'x'.

Reorder the terms:
-10 + 22 + -11x + -6x + 6x2 = -22 + 6x + 22 + -6x

Combine like terms: -10 + 22 = 12
12 + -11x + -6x + 6x2 = -22 + 6x + 22 + -6x

Combine like terms: -11x + -6x = -17x
12 + -17x + 6x2 = -22 + 6x + 22 + -6x

Reorder the terms:
12 + -17x + 6x2 = -22 + 22 + 6x + -6x

Combine like terms: -22 + 22 = 0
12 + -17x + 6x2 = 0 + 6x + -6x
12 + -17x + 6x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
12 + -17x + 6x2 = 0

Factor a trinomial.
(4 + -3x)(3 + -2x) = 0


Subproblem 1
Set the factor '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333

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 = {1.333333333, 1.5}

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