10x^2+35x+10=3x^2-2x

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Solution for 10x^2+35x+10=3x^2-2x equation: 


Simplifying
10x2 + 35x + 10 = 3x2 + -2x

Reorder the terms:
10 + 35x + 10x2 = 3x2 + -2x

Reorder the terms:
10 + 35x + 10x2 = -2x + 3x2

Solving
10 + 35x + 10x2 = -2x + 3x2

Solving for variable 'x'.

Reorder the terms:
10 + 35x + 2x + 10x2 + -3x2 = -2x + 3x2 + 2x + -3x2

Combine like terms: 35x + 2x = 37x
10 + 37x + 10x2 + -3x2 = -2x + 3x2 + 2x + -3x2

Combine like terms: 10x2 + -3x2 = 7x2
10 + 37x + 7x2 = -2x + 3x2 + 2x + -3x2

Reorder the terms:
10 + 37x + 7x2 = -2x + 2x + 3x2 + -3x2

Combine like terms: -2x + 2x = 0
10 + 37x + 7x2 = 0 + 3x2 + -3x2
10 + 37x + 7x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
10 + 37x + 7x2 = 0

Factor a trinomial.
(5 + x)(2 + 7x) = 0


Subproblem 1
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

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

Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5

Subproblem 2
Set the factor '(2 + 7x)' equal to zero and attempt to solve:

Simplifying
2 + 7x = 0

Solving
2 + 7x = 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 + 7x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 7x = 0 + -2
7x = 0 + -2

Combine like terms: 0 + -2 = -2
7x = -2

Divide each side by '7'.
x = -0.2857142857

Simplifying
x = -0.2857142857
Solution
x = {-5, -0.2857142857}

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