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

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


Simplifying
x2 + 14x = 5x2 + -5x + -5

Reorder the terms:
14x + x2 = 5x2 + -5x + -5

Reorder the terms:
14x + x2 = -5 + -5x + 5x2

Solving
14x + x2 = -5 + -5x + 5x2

Solving for variable 'x'.

Reorder the terms:
5 + 14x + 5x + x2 + -5x2 = -5 + -5x + 5x2 + 5 + 5x + -5x2

Combine like terms: 14x + 5x = 19x
5 + 19x + x2 + -5x2 = -5 + -5x + 5x2 + 5 + 5x + -5x2

Combine like terms: x2 + -5x2 = -4x2
5 + 19x + -4x2 = -5 + -5x + 5x2 + 5 + 5x + -5x2

Reorder the terms:
5 + 19x + -4x2 = -5 + 5 + -5x + 5x + 5x2 + -5x2

Combine like terms: -5 + 5 = 0
5 + 19x + -4x2 = 0 + -5x + 5x + 5x2 + -5x2
5 + 19x + -4x2 = -5x + 5x + 5x2 + -5x2

Combine like terms: -5x + 5x = 0
5 + 19x + -4x2 = 0 + 5x2 + -5x2
5 + 19x + -4x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
5 + 19x + -4x2 = 0

Factor a trinomial.
(5 + -1x)(1 + 4x) = 0


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

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5

Subproblem 2
Set the factor '(1 + 4x)' equal to zero and attempt to solve:

Simplifying
1 + 4x = 0

Solving
1 + 4x = 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 + 4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4x = 0 + -1
4x = 0 + -1

Combine like terms: 0 + -1 = -1
4x = -1

Divide each side by '4'.
x = -0.25

Simplifying
x = -0.25
Solution
x = {5, -0.25}

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