3x^2-5x+7=2x^2-2x+11

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Solution for 3x^2-5x+7=2x^2-2x+11 equation:


Simplifying
3x2 + -5x + 7 = 2x2 + -2x + 11

Reorder the terms:
7 + -5x + 3x2 = 2x2 + -2x + 11

Reorder the terms:
7 + -5x + 3x2 = 11 + -2x + 2x2

Solving
7 + -5x + 3x2 = 11 + -2x + 2x2

Solving for variable 'x'.

Reorder the terms:
7 + -11 + -5x + 2x + 3x2 + -2x2 = 11 + -2x + 2x2 + -11 + 2x + -2x2

Combine like terms: 7 + -11 = -4
-4 + -5x + 2x + 3x2 + -2x2 = 11 + -2x + 2x2 + -11 + 2x + -2x2

Combine like terms: -5x + 2x = -3x
-4 + -3x + 3x2 + -2x2 = 11 + -2x + 2x2 + -11 + 2x + -2x2

Combine like terms: 3x2 + -2x2 = 1x2
-4 + -3x + 1x2 = 11 + -2x + 2x2 + -11 + 2x + -2x2

Reorder the terms:
-4 + -3x + 1x2 = 11 + -11 + -2x + 2x + 2x2 + -2x2

Combine like terms: 11 + -11 = 0
-4 + -3x + 1x2 = 0 + -2x + 2x + 2x2 + -2x2
-4 + -3x + 1x2 = -2x + 2x + 2x2 + -2x2

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

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

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

Solution

x = {-1, 4}

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