5x^2+6=14x+9

Solution for 5x^2+6=14x+9 equation:

Simplifying
5x2 + 6 = 14x + 9

Reorder the terms:
6 + 5x2 = 14x + 9

Reorder the terms:
6 + 5x2 = 9 + 14x

Solving
6 + 5x2 = 9 + 14x

Solving for variable 'x'.

Reorder the terms:
6 + -9 + -14x + 5x2 = 9 + 14x + -9 + -14x

Combine like terms: 6 + -9 = -3
-3 + -14x + 5x2 = 9 + 14x + -9 + -14x

Reorder the terms:
-3 + -14x + 5x2 = 9 + -9 + 14x + -14x

Combine like terms: 9 + -9 = 0
-3 + -14x + 5x2 = 0 + 14x + -14x
-3 + -14x + 5x2 = 14x + -14x

Combine like terms: 14x + -14x = 0
-3 + -14x + 5x2 = 0

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

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

Simplifying
-1 + -5x = 0

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

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

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

Divide each side by '-5'.
x = -0.2

Simplifying
x = -0.2
Subproblem 2
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
Solution
x = {-0.2, 3}