7x^2+6=18x-5x^2

Solution for 7x^2+6=18x-5x^2 equation:

Simplifying
7x2 + 6 = 18x + -5x2

Reorder the terms:
6 + 7x2 = 18x + -5x2

Solving
6 + 7x2 = 18x + -5x2

Solving for variable 'x'.

Reorder the terms:
6 + -18x + 7x2 + 5x2 = 18x + -5x2 + -18x + 5x2

Combine like terms: 7x2 + 5x2 = 12x2
6 + -18x + 12x2 = 18x + -5x2 + -18x + 5x2

Reorder the terms:
6 + -18x + 12x2 = 18x + -18x + -5x2 + 5x2

Combine like terms: 18x + -18x = 0
6 + -18x + 12x2 = 0 + -5x2 + 5x2
6 + -18x + 12x2 = -5x2 + 5x2

Combine like terms: -5x2 + 5x2 = 0
6 + -18x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(1 + -3x + 2x2) = 0

Factor a trinomial.
6((1 + -2x)(1 + -1x)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
Solution
x = {0.5, 1}