11x^2-12x+11=8x^2+4-2x

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Solution for 11x^2-12x+11=8x^2+4-2x equation:


Simplifying
11x2 + -12x + 11 = 8x2 + 4 + -2x

Reorder the terms:
11 + -12x + 11x2 = 8x2 + 4 + -2x

Reorder the terms:
11 + -12x + 11x2 = 4 + -2x + 8x2

Solving
11 + -12x + 11x2 = 4 + -2x + 8x2

Solving for variable 'x'.

Reorder the terms:
11 + -4 + -12x + 2x + 11x2 + -8x2 = 4 + -2x + 8x2 + -4 + 2x + -8x2

Combine like terms: 11 + -4 = 7
7 + -12x + 2x + 11x2 + -8x2 = 4 + -2x + 8x2 + -4 + 2x + -8x2

Combine like terms: -12x + 2x = -10x
7 + -10x + 11x2 + -8x2 = 4 + -2x + 8x2 + -4 + 2x + -8x2

Combine like terms: 11x2 + -8x2 = 3x2
7 + -10x + 3x2 = 4 + -2x + 8x2 + -4 + 2x + -8x2

Reorder the terms:
7 + -10x + 3x2 = 4 + -4 + -2x + 2x + 8x2 + -8x2

Combine like terms: 4 + -4 = 0
7 + -10x + 3x2 = 0 + -2x + 2x + 8x2 + -8x2
7 + -10x + 3x2 = -2x + 2x + 8x2 + -8x2

Combine like terms: -2x + 2x = 0
7 + -10x + 3x2 = 0 + 8x2 + -8x2
7 + -10x + 3x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
7 + -10x + 3x2 = 0

Factor a trinomial.
(1 + -1x)(7 + -3x) = 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 '(7 + -3x)' equal to zero and attempt to solve: Simplifying 7 + -3x = 0 Solving 7 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -3x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3x = 0 + -7 -3x = 0 + -7 Combine like terms: 0 + -7 = -7 -3x = -7 Divide each side by '-3'. x = 2.333333333 Simplifying x = 2.333333333

Solution

x = {1, 2.333333333}

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