-x^2+3x=-4x+6

Solution for -x^2+3x=-4x+6 equation:

Simplifying
-1x2 + 3x = -4x + 6

Reorder the terms:
3x + -1x2 = -4x + 6

Reorder the terms:
3x + -1x2 = 6 + -4x

Solving
3x + -1x2 = 6 + -4x

Solving for variable 'x'.

Reorder the terms:
-6 + 3x + 4x + -1x2 = 6 + -4x + -6 + 4x

Combine like terms: 3x + 4x = 7x
-6 + 7x + -1x2 = 6 + -4x + -6 + 4x

Reorder the terms:
-6 + 7x + -1x2 = 6 + -6 + -4x + 4x

Combine like terms: 6 + -6 = 0
-6 + 7x + -1x2 = 0 + -4x + 4x
-6 + 7x + -1x2 = -4x + 4x

Combine like terms: -4x + 4x = 0
-6 + 7x + -1x2 = 0

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

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

Simplifying
-6 + x = 0

Solving
-6 + x = 0

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

Add '6' to each side of the equation.
-6 + 6 + x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + x = 0 + 6
x = 0 + 6

Combine like terms: 0 + 6 = 6
x = 6

Simplifying
x = 6
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 = {6, 1}