x^2+14x+10=-x^2+3x+5

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Solution for x^2+14x+10=-x^2+3x+5 equation:


Simplifying
x2 + 14x + 10 = -1x2 + 3x + 5

Reorder the terms:
10 + 14x + x2 = -1x2 + 3x + 5

Reorder the terms:
10 + 14x + x2 = 5 + 3x + -1x2

Solving
10 + 14x + x2 = 5 + 3x + -1x2

Solving for variable 'x'.

Reorder the terms:
10 + -5 + 14x + -3x + x2 + x2 = 5 + 3x + -1x2 + -5 + -3x + x2

Combine like terms: 10 + -5 = 5
5 + 14x + -3x + x2 + x2 = 5 + 3x + -1x2 + -5 + -3x + x2

Combine like terms: 14x + -3x = 11x
5 + 11x + x2 + x2 = 5 + 3x + -1x2 + -5 + -3x + x2

Combine like terms: x2 + x2 = 2x2
5 + 11x + 2x2 = 5 + 3x + -1x2 + -5 + -3x + x2

Reorder the terms:
5 + 11x + 2x2 = 5 + -5 + 3x + -3x + -1x2 + x2

Combine like terms: 5 + -5 = 0
5 + 11x + 2x2 = 0 + 3x + -3x + -1x2 + x2
5 + 11x + 2x2 = 3x + -3x + -1x2 + x2

Combine like terms: 3x + -3x = 0
5 + 11x + 2x2 = 0 + -1x2 + x2
5 + 11x + 2x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
5 + 11x + 2x2 = 0

Factor a trinomial.
(5 + x)(1 + 2x) = 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 '(1 + 2x)' equal to zero and attempt to solve:

Simplifying
1 + 2x = 0

Solving
1 + 2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2x = 0 + -1
2x = 0 + -1

Combine like terms: 0 + -1 = -1
2x = -1

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5
Solution
x = {-5, -0.5}

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