(3x+1)(2x-3)=x(2x-11)

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Solution for (3x+1)(2x-3)=x(2x-11) equation: 


Simplifying
(3x + 1)(2x + -3) = x(2x + -11)

Reorder the terms:
(1 + 3x)(2x + -3) = x(2x + -11)

Reorder the terms:
(1 + 3x)(-3 + 2x) = x(2x + -11)

Multiply (1 + 3x) * (-3 + 2x)
(1(-3 + 2x) + 3x * (-3 + 2x)) = x(2x + -11)
((-3 * 1 + 2x * 1) + 3x * (-3 + 2x)) = x(2x + -11)
((-3 + 2x) + 3x * (-3 + 2x)) = x(2x + -11)
(-3 + 2x + (-3 * 3x + 2x * 3x)) = x(2x + -11)
(-3 + 2x + (-9x + 6x2)) = x(2x + -11)

Combine like terms: 2x + -9x = -7x
(-3 + -7x + 6x2) = x(2x + -11)

Reorder the terms:
-3 + -7x + 6x2 = x(-11 + 2x)
-3 + -7x + 6x2 = (-11 * x + 2x * x)
-3 + -7x + 6x2 = (-11x + 2x2)

Solving
-3 + -7x + 6x2 = -11x + 2x2

Solving for variable 'x'.

Reorder the terms:
-3 + -7x + 11x + 6x2 + -2x2 = -11x + 2x2 + 11x + -2x2

Combine like terms: -7x + 11x = 4x
-3 + 4x + 6x2 + -2x2 = -11x + 2x2 + 11x + -2x2

Combine like terms: 6x2 + -2x2 = 4x2
-3 + 4x + 4x2 = -11x + 2x2 + 11x + -2x2

Reorder the terms:
-3 + 4x + 4x2 = -11x + 11x + 2x2 + -2x2

Combine like terms: -11x + 11x = 0
-3 + 4x + 4x2 = 0 + 2x2 + -2x2
-3 + 4x + 4x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-3 + 4x + 4x2 = 0

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


Subproblem 1
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

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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {-1.5, 0.5}

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