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

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


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

Reorder the terms:
2x(3 + x) = (x + 1)(x + -2) + -10
(3 * 2x + x * 2x) = (x + 1)(x + -2) + -10
(6x + 2x2) = (x + 1)(x + -2) + -10

Reorder the terms:
6x + 2x2 = (1 + x)(x + -2) + -10

Reorder the terms:
6x + 2x2 = (1 + x)(-2 + x) + -10

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

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

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

Combine like terms: -2 + -10 = -12
6x + 2x2 = -12 + -1x + x2

Solving
6x + 2x2 = -12 + -1x + x2

Solving for variable 'x'.

Reorder the terms:
12 + 6x + x + 2x2 + -1x2 = -12 + -1x + x2 + 12 + x + -1x2

Combine like terms: 6x + x = 7x
12 + 7x + 2x2 + -1x2 = -12 + -1x + x2 + 12 + x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
12 + 7x + 1x2 = -12 + -1x + x2 + 12 + x + -1x2

Reorder the terms:
12 + 7x + 1x2 = -12 + 12 + -1x + x + x2 + -1x2

Combine like terms: -12 + 12 = 0
12 + 7x + 1x2 = 0 + -1x + x + x2 + -1x2
12 + 7x + 1x2 = -1x + x + x2 + -1x2

Combine like terms: -1x + x = 0
12 + 7x + 1x2 = 0 + x2 + -1x2
12 + 7x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
12 + 7x + 1x2 = 0

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


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

Simplifying
4 + x = 0

Solving
4 + x = 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 + x = 0 + -4

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

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

Simplifying
x = -4

Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

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

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

Simplifying
x = -3
Solution
x = {-4, -3}

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