x^2+13x+7=-x^2+4x

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Solution for x^2+13x+7=-x^2+4x equation: 


Simplifying
x2 + 13x + 7 = -1x2 + 4x

Reorder the terms:
7 + 13x + x2 = -1x2 + 4x

Reorder the terms:
7 + 13x + x2 = 4x + -1x2

Solving
7 + 13x + x2 = 4x + -1x2

Solving for variable 'x'.

Reorder the terms:
7 + 13x + -4x + x2 + x2 = 4x + -1x2 + -4x + x2

Combine like terms: 13x + -4x = 9x
7 + 9x + x2 + x2 = 4x + -1x2 + -4x + x2

Combine like terms: x2 + x2 = 2x2
7 + 9x + 2x2 = 4x + -1x2 + -4x + x2

Reorder the terms:
7 + 9x + 2x2 = 4x + -4x + -1x2 + x2

Combine like terms: 4x + -4x = 0
7 + 9x + 2x2 = 0 + -1x2 + x2
7 + 9x + 2x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
7 + 9x + 2x2 = 0

Factor a trinomial.
(7 + 2x)(1 + x) = 0


Subproblem 1
Set the factor '(7 + 2x)' equal to zero and attempt to solve:

Simplifying
7 + 2x = 0

Solving
7 + 2x = 0

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

Add '-7' to each side of the equation.
7 + -7 + 2x = 0 + -7

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

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

Divide each side by '2'.
x = -3.5

Simplifying
x = -3.5

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

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

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

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

Simplifying
x = -1
Solution
x = {-3.5, -1}

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