7x^2+6=17x-5x^2

Solution for 7x^2+6=17x-5x^2 equation:

Simplifying
7x2 + 6 = 17x + -5x2

Reorder the terms:
6 + 7x2 = 17x + -5x2

Solving
6 + 7x2 = 17x + -5x2

Solving for variable 'x'.

Reorder the terms:
6 + -17x + 7x2 + 5x2 = 17x + -5x2 + -17x + 5x2

Combine like terms: 7x2 + 5x2 = 12x2
6 + -17x + 12x2 = 17x + -5x2 + -17x + 5x2

Reorder the terms:
6 + -17x + 12x2 = 17x + -17x + -5x2 + 5x2

Combine like terms: 17x + -17x = 0
6 + -17x + 12x2 = 0 + -5x2 + 5x2
6 + -17x + 12x2 = -5x2 + 5x2

Combine like terms: -5x2 + 5x2 = 0
6 + -17x + 12x2 = 0

Factor a trinomial.
(2 + -3x)(3 + -4x) = 0

Subproblem 1
Set the factor '(2 + -3x)' equal to zero and attempt to solve:

Simplifying
2 + -3x = 0

Solving
2 + -3x = 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 + -3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3x = 0 + -2
-3x = 0 + -2

Combine like terms: 0 + -2 = -2
-3x = -2

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667
Subproblem 2
Set the factor '(3 + -4x)' equal to zero and attempt to solve:

Simplifying
3 + -4x = 0

Solving
3 + -4x = 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 + -4x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4x = 0 + -3
-4x = 0 + -3

Combine like terms: 0 + -3 = -3
-4x = -3

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75
Solution
x = {0.6666666667, 0.75}