2x^2=6x-4

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Solution for 2x^2=6x-4 equation:


Simplifying
2x2 = 6x + -4

Reorder the terms:
2x2 = -4 + 6x

Solving
2x2 = -4 + 6x

Solving for variable 'x'.

Reorder the terms:
4 + -6x + 2x2 = -4 + 6x + 4 + -6x

Reorder the terms:
4 + -6x + 2x2 = -4 + 4 + 6x + -6x

Combine like terms: -4 + 4 = 0
4 + -6x + 2x2 = 0 + 6x + -6x
4 + -6x + 2x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
4 + -6x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + -3x + x2) = 0

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

Ignore the factor 2.

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 '(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 = {1, 2}

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