3x^2-21=2x^2-4x

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Solution for 3x^2-21=2x^2-4x equation:


Simplifying
3x2 + -21 = 2x2 + -4x

Reorder the terms:
-21 + 3x2 = 2x2 + -4x

Reorder the terms:
-21 + 3x2 = -4x + 2x2

Solving
-21 + 3x2 = -4x + 2x2

Solving for variable 'x'.

Reorder the terms:
-21 + 4x + 3x2 + -2x2 = -4x + 2x2 + 4x + -2x2

Combine like terms: 3x2 + -2x2 = 1x2
-21 + 4x + 1x2 = -4x + 2x2 + 4x + -2x2

Reorder the terms:
-21 + 4x + 1x2 = -4x + 4x + 2x2 + -2x2

Combine like terms: -4x + 4x = 0
-21 + 4x + 1x2 = 0 + 2x2 + -2x2
-21 + 4x + 1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-21 + 4x + 1x2 = 0

Factor a trinomial.
(-7 + -1x)(3 + -1x) = 0

Subproblem 1

Set the factor '(-7 + -1x)' equal to zero and attempt to solve: Simplifying -7 + -1x = 0 Solving -7 + -1x = 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 + -1x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1x = 0 + 7 -1x = 0 + 7 Combine like terms: 0 + 7 = 7 -1x = 7 Divide each side by '-1'. x = -7 Simplifying x = -7

Subproblem 2

Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3

Solution

x = {-7, 3}

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