7x^2=1-6x

Solution for 7x^2=1-6x equation:

Simplifying
7x2 = 1 + -6x

Solving
7x2 = 1 + -6x

Solving for variable 'x'.

Reorder the terms:
-1 + 6x + 7x2 = 1 + -6x + -1 + 6x

Reorder the terms:
-1 + 6x + 7x2 = 1 + -1 + -6x + 6x

Combine like terms: 1 + -1 = 0
-1 + 6x + 7x2 = 0 + -6x + 6x
-1 + 6x + 7x2 = -6x + 6x

Combine like terms: -6x + 6x = 0
-1 + 6x + 7x2 = 0

Factor a trinomial.
(-1 + -1x)(1 + -7x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(1 + -7x)' equal to zero and attempt to solve:

Simplifying
1 + -7x = 0

Solving
1 + -7x = 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 + -7x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -7x = 0 + -1
-7x = 0 + -1

Combine like terms: 0 + -1 = -1
-7x = -1

Divide each side by '-7'.
x = 0.1428571429

Simplifying
x = 0.1428571429
Solution
x = {-1, 0.1428571429}