7x-1=x^2+3x+2

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Solution for 7x-1=x^2+3x+2 equation:


Simplifying
7x + -1 = x2 + 3x + 2

Reorder the terms:
-1 + 7x = x2 + 3x + 2

Reorder the terms:
-1 + 7x = 2 + 3x + x2

Solving
-1 + 7x = 2 + 3x + x2

Solving for variable 'x'.

Reorder the terms:
-1 + -2 + 7x + -3x + -1x2 = 2 + 3x + x2 + -2 + -3x + -1x2

Combine like terms: -1 + -2 = -3
-3 + 7x + -3x + -1x2 = 2 + 3x + x2 + -2 + -3x + -1x2

Combine like terms: 7x + -3x = 4x
-3 + 4x + -1x2 = 2 + 3x + x2 + -2 + -3x + -1x2

Reorder the terms:
-3 + 4x + -1x2 = 2 + -2 + 3x + -3x + x2 + -1x2

Combine like terms: 2 + -2 = 0
-3 + 4x + -1x2 = 0 + 3x + -3x + x2 + -1x2
-3 + 4x + -1x2 = 3x + -3x + x2 + -1x2

Combine like terms: 3x + -3x = 0
-3 + 4x + -1x2 = 0 + x2 + -1x2
-3 + 4x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-3 + 4x + -1x2 = 0

Factor a trinomial.
(-3 + x)(1 + -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 '(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 = {3, 1}

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