3x^2+7x+10=2x^2-5x-10

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Solution for 3x^2+7x+10=2x^2-5x-10 equation: 


Simplifying
3x2 + 7x + 10 = 2x2 + -5x + -10

Reorder the terms:
10 + 7x + 3x2 = 2x2 + -5x + -10

Reorder the terms:
10 + 7x + 3x2 = -10 + -5x + 2x2

Solving
10 + 7x + 3x2 = -10 + -5x + 2x2

Solving for variable 'x'.

Reorder the terms:
10 + 10 + 7x + 5x + 3x2 + -2x2 = -10 + -5x + 2x2 + 10 + 5x + -2x2

Combine like terms: 10 + 10 = 20
20 + 7x + 5x + 3x2 + -2x2 = -10 + -5x + 2x2 + 10 + 5x + -2x2

Combine like terms: 7x + 5x = 12x
20 + 12x + 3x2 + -2x2 = -10 + -5x + 2x2 + 10 + 5x + -2x2

Combine like terms: 3x2 + -2x2 = 1x2
20 + 12x + 1x2 = -10 + -5x + 2x2 + 10 + 5x + -2x2

Reorder the terms:
20 + 12x + 1x2 = -10 + 10 + -5x + 5x + 2x2 + -2x2

Combine like terms: -10 + 10 = 0
20 + 12x + 1x2 = 0 + -5x + 5x + 2x2 + -2x2
20 + 12x + 1x2 = -5x + 5x + 2x2 + -2x2

Combine like terms: -5x + 5x = 0
20 + 12x + 1x2 = 0 + 2x2 + -2x2
20 + 12x + 1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
20 + 12x + 1x2 = 0

Factor a trinomial.
(10 + x)(2 + x) = 0


Subproblem 1
Set the factor '(10 + x)' equal to zero and attempt to solve:

Simplifying
10 + x = 0

Solving
10 + x = 0

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

Add '-10' to each side of the equation.
10 + -10 + x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + x = 0 + -10
x = 0 + -10

Combine like terms: 0 + -10 = -10
x = -10

Simplifying
x = -10

Subproblem 2
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
Solution
x = {-10, -2}

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