(2x-5)(x+1)=3(2x-1)-11

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Solution for (2x-5)(x+1)=3(2x-1)-11 equation: 


Simplifying
(2x + -5)(x + 1) = 3(2x + -1) + -11

Reorder the terms:
(-5 + 2x)(x + 1) = 3(2x + -1) + -11

Reorder the terms:
(-5 + 2x)(1 + x) = 3(2x + -1) + -11

Multiply (-5 + 2x) * (1 + x)
(-5(1 + x) + 2x * (1 + x)) = 3(2x + -1) + -11
((1 * -5 + x * -5) + 2x * (1 + x)) = 3(2x + -1) + -11
((-5 + -5x) + 2x * (1 + x)) = 3(2x + -1) + -11
(-5 + -5x + (1 * 2x + x * 2x)) = 3(2x + -1) + -11
(-5 + -5x + (2x + 2x2)) = 3(2x + -1) + -11

Combine like terms: -5x + 2x = -3x
(-5 + -3x + 2x2) = 3(2x + -1) + -11

Reorder the terms:
-5 + -3x + 2x2 = 3(-1 + 2x) + -11
-5 + -3x + 2x2 = (-1 * 3 + 2x * 3) + -11
-5 + -3x + 2x2 = (-3 + 6x) + -11

Reorder the terms:
-5 + -3x + 2x2 = -3 + -11 + 6x

Combine like terms: -3 + -11 = -14
-5 + -3x + 2x2 = -14 + 6x

Solving
-5 + -3x + 2x2 = -14 + 6x

Solving for variable 'x'.

Reorder the terms:
-5 + 14 + -3x + -6x + 2x2 = -14 + 6x + 14 + -6x

Combine like terms: -5 + 14 = 9
9 + -3x + -6x + 2x2 = -14 + 6x + 14 + -6x

Combine like terms: -3x + -6x = -9x
9 + -9x + 2x2 = -14 + 6x + 14 + -6x

Reorder the terms:
9 + -9x + 2x2 = -14 + 14 + 6x + -6x

Combine like terms: -14 + 14 = 0
9 + -9x + 2x2 = 0 + 6x + -6x
9 + -9x + 2x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
9 + -9x + 2x2 = 0

Factor a trinomial.
(3 + -2x)(3 + -1x) = 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 '(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
Solution
x = {1.5, 3}

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