5x^2+14x=x+6

Solution for 5x^2+14x=x+6 equation:

Simplifying
5x2 + 14x = x + 6

Reorder the terms:
14x + 5x2 = x + 6

Reorder the terms:
14x + 5x2 = 6 + x

Solving
14x + 5x2 = 6 + x

Solving for variable 'x'.

Reorder the terms:
-6 + 14x + -1x + 5x2 = 6 + x + -6 + -1x

Combine like terms: 14x + -1x = 13x
-6 + 13x + 5x2 = 6 + x + -6 + -1x

Reorder the terms:
-6 + 13x + 5x2 = 6 + -6 + x + -1x

Combine like terms: 6 + -6 = 0
-6 + 13x + 5x2 = 0 + x + -1x
-6 + 13x + 5x2 = x + -1x

Combine like terms: x + -1x = 0
-6 + 13x + 5x2 = 0

Factor a trinomial.
(-3 + -1x)(2 + -5x) = 0

Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3
Subproblem 2
Set the factor '(2 + -5x)' equal to zero and attempt to solve:

Simplifying
2 + -5x = 0

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

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

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

Divide each side by '-5'.
x = 0.4

Simplifying
x = 0.4
Solution
x = {-3, 0.4}