2x^2+1-3=-6(x-1)

Solution for 2x^2+1-3=-6(x-1) equation:

Simplifying
2x2 + 1 + -3 = -6(x + -1)

Reorder the terms:
1 + -3 + 2x2 = -6(x + -1)

Combine like terms: 1 + -3 = -2
-2 + 2x2 = -6(x + -1)

Reorder the terms:
-2 + 2x2 = -6(-1 + x)
-2 + 2x2 = (-1 * -6 + x * -6)
-2 + 2x2 = (6 + -6x)

Solving
-2 + 2x2 = 6 + -6x

Solving for variable 'x'.

Reorder the terms:
-2 + -6 + 6x + 2x2 = 6 + -6x + -6 + 6x

Combine like terms: -2 + -6 = -8
-8 + 6x + 2x2 = 6 + -6x + -6 + 6x

Reorder the terms:
-8 + 6x + 2x2 = 6 + -6 + -6x + 6x

Combine like terms: 6 + -6 = 0
-8 + 6x + 2x2 = 0 + -6x + 6x
-8 + 6x + 2x2 = -6x + 6x

Combine like terms: -6x + 6x = 0
-8 + 6x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + 3x + x2) = 0

Factor a trinomial.
2((-4 + -1x)(1 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4
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 = {-4, 1}