-x+4=x^2-6x+10

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Solution for -x+4=x^2-6x+10 equation:


Simplifying
-1x + 4 = x2 + -6x + 10

Reorder the terms:
4 + -1x = x2 + -6x + 10

Reorder the terms:
4 + -1x = 10 + -6x + x2

Solving
4 + -1x = 10 + -6x + x2

Solving for variable 'x'.

Reorder the terms:
4 + -10 + -1x + 6x + -1x2 = 10 + -6x + x2 + -10 + 6x + -1x2

Combine like terms: 4 + -10 = -6
-6 + -1x + 6x + -1x2 = 10 + -6x + x2 + -10 + 6x + -1x2

Combine like terms: -1x + 6x = 5x
-6 + 5x + -1x2 = 10 + -6x + x2 + -10 + 6x + -1x2

Reorder the terms:
-6 + 5x + -1x2 = 10 + -10 + -6x + 6x + x2 + -1x2

Combine like terms: 10 + -10 = 0
-6 + 5x + -1x2 = 0 + -6x + 6x + x2 + -1x2
-6 + 5x + -1x2 = -6x + 6x + x2 + -1x2

Combine like terms: -6x + 6x = 0
-6 + 5x + -1x2 = 0 + x2 + -1x2
-6 + 5x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-6 + 5x + -1x2 = 0

Factor a trinomial.
(-3 + x)(2 + -1x) = 0

Subproblem 1

Set the factor '(-3 + x)' equal to zero and attempt to solve: Simplifying -3 + x = 0 Solving -3 + x = 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 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Simplifying x = 3

Subproblem 2

Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2

Solution

x = {3, 2}

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