3x^2+8x=x^2-x-10

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Solution for 3x^2+8x=x^2-x-10 equation: 


Simplifying
3x2 + 8x = x2 + -1x + -10

Reorder the terms:
8x + 3x2 = x2 + -1x + -10

Reorder the terms:
8x + 3x2 = -10 + -1x + x2

Solving
8x + 3x2 = -10 + -1x + x2

Solving for variable 'x'.

Reorder the terms:
10 + 8x + x + 3x2 + -1x2 = -10 + -1x + x2 + 10 + x + -1x2

Combine like terms: 8x + x = 9x
10 + 9x + 3x2 + -1x2 = -10 + -1x + x2 + 10 + x + -1x2

Combine like terms: 3x2 + -1x2 = 2x2
10 + 9x + 2x2 = -10 + -1x + x2 + 10 + x + -1x2

Reorder the terms:
10 + 9x + 2x2 = -10 + 10 + -1x + x + x2 + -1x2

Combine like terms: -10 + 10 = 0
10 + 9x + 2x2 = 0 + -1x + x + x2 + -1x2
10 + 9x + 2x2 = -1x + x + x2 + -1x2

Combine like terms: -1x + x = 0
10 + 9x + 2x2 = 0 + x2 + -1x2
10 + 9x + 2x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
10 + 9x + 2x2 = 0

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


Subproblem 1
Set the factor '(5 + 2x)' equal to zero and attempt to solve:

Simplifying
5 + 2x = 0

Solving
5 + 2x = 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 + 2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2x = 0 + -5
2x = 0 + -5

Combine like terms: 0 + -5 = -5
2x = -5

Divide each side by '2'.
x = -2.5

Simplifying
x = -2.5

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 = {-2.5, -2}

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