12+2x-10x=x^2+28

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Solution for 12+2x-10x=x^2+28 equation:


Simplifying
12 + 2x + -10x = x2 + 28

Combine like terms: 2x + -10x = -8x
12 + -8x = x2 + 28

Reorder the terms:
12 + -8x = 28 + x2

Solving
12 + -8x = 28 + x2

Solving for variable 'x'.

Reorder the terms:
12 + -28 + -8x + -1x2 = 28 + x2 + -28 + -1x2

Combine like terms: 12 + -28 = -16
-16 + -8x + -1x2 = 28 + x2 + -28 + -1x2

Reorder the terms:
-16 + -8x + -1x2 = 28 + -28 + x2 + -1x2

Combine like terms: 28 + -28 = 0
-16 + -8x + -1x2 = 0 + x2 + -1x2
-16 + -8x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-16 + -8x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(16 + 8x + x2) = 0

Factor a trinomial.
-1((4 + x)(4 + x)) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4

Subproblem 2

Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4

Solution

x = {-4, -4}

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