(3x-2)(2x+1)=3x^2-11x-10

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Solution for (3x-2)(2x+1)=3x^2-11x-10 equation: 


Simplifying
(3x + -2)(2x + 1) = 3x2 + -11x + -10

Reorder the terms:
(-2 + 3x)(2x + 1) = 3x2 + -11x + -10

Reorder the terms:
(-2 + 3x)(1 + 2x) = 3x2 + -11x + -10

Multiply (-2 + 3x) * (1 + 2x)
(-2(1 + 2x) + 3x * (1 + 2x)) = 3x2 + -11x + -10
((1 * -2 + 2x * -2) + 3x * (1 + 2x)) = 3x2 + -11x + -10
((-2 + -4x) + 3x * (1 + 2x)) = 3x2 + -11x + -10
(-2 + -4x + (1 * 3x + 2x * 3x)) = 3x2 + -11x + -10
(-2 + -4x + (3x + 6x2)) = 3x2 + -11x + -10

Combine like terms: -4x + 3x = -1x
(-2 + -1x + 6x2) = 3x2 + -11x + -10

Reorder the terms:
-2 + -1x + 6x2 = -10 + -11x + 3x2

Solving
-2 + -1x + 6x2 = -10 + -11x + 3x2

Solving for variable 'x'.

Reorder the terms:
-2 + 10 + -1x + 11x + 6x2 + -3x2 = -10 + -11x + 3x2 + 10 + 11x + -3x2

Combine like terms: -2 + 10 = 8
8 + -1x + 11x + 6x2 + -3x2 = -10 + -11x + 3x2 + 10 + 11x + -3x2

Combine like terms: -1x + 11x = 10x
8 + 10x + 6x2 + -3x2 = -10 + -11x + 3x2 + 10 + 11x + -3x2

Combine like terms: 6x2 + -3x2 = 3x2
8 + 10x + 3x2 = -10 + -11x + 3x2 + 10 + 11x + -3x2

Reorder the terms:
8 + 10x + 3x2 = -10 + 10 + -11x + 11x + 3x2 + -3x2

Combine like terms: -10 + 10 = 0
8 + 10x + 3x2 = 0 + -11x + 11x + 3x2 + -3x2
8 + 10x + 3x2 = -11x + 11x + 3x2 + -3x2

Combine like terms: -11x + 11x = 0
8 + 10x + 3x2 = 0 + 3x2 + -3x2
8 + 10x + 3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
8 + 10x + 3x2 = 0

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


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

Simplifying
2 + x = 0

Solving
2 + x = 0

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

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

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

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

Simplifying
x = -2

Subproblem 2
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
Solution
x = {-2, -1.333333333}

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