2x^2=12x-10

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Solution for 2x^2=12x-10 equation:


Simplifying
2x2 = 12x + -10

Reorder the terms:
2x2 = -10 + 12x

Solving
2x2 = -10 + 12x

Solving for variable 'x'.

Reorder the terms:
10 + -12x + 2x2 = -10 + 12x + 10 + -12x

Reorder the terms:
10 + -12x + 2x2 = -10 + 10 + 12x + -12x

Combine like terms: -10 + 10 = 0
10 + -12x + 2x2 = 0 + 12x + -12x
10 + -12x + 2x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
10 + -12x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + -6x + x2) = 0

Factor a trinomial.
2((1 + -1x)(5 + -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 '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5

Solution

x = {1, 5}

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