3x^2-4x+20=2x^2+16

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Solution for 3x^2-4x+20=2x^2+16 equation:


Simplifying
3x2 + -4x + 20 = 2x2 + 16

Reorder the terms:
20 + -4x + 3x2 = 2x2 + 16

Reorder the terms:
20 + -4x + 3x2 = 16 + 2x2

Solving
20 + -4x + 3x2 = 16 + 2x2

Solving for variable 'x'.

Reorder the terms:
20 + -16 + -4x + 3x2 + -2x2 = 16 + 2x2 + -16 + -2x2

Combine like terms: 20 + -16 = 4
4 + -4x + 3x2 + -2x2 = 16 + 2x2 + -16 + -2x2

Combine like terms: 3x2 + -2x2 = 1x2
4 + -4x + 1x2 = 16 + 2x2 + -16 + -2x2

Reorder the terms:
4 + -4x + 1x2 = 16 + -16 + 2x2 + -2x2

Combine like terms: 16 + -16 = 0
4 + -4x + 1x2 = 0 + 2x2 + -2x2
4 + -4x + 1x2 = 2x2 + -2x2

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

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

Subproblem 1

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

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 = {2, 2}

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