x^2-3x+16=4-10x

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Solution for x^2-3x+16=4-10x equation:


Simplifying
x2 + -3x + 16 = 4 + -10x

Reorder the terms:
16 + -3x + x2 = 4 + -10x

Solving
16 + -3x + x2 = 4 + -10x

Solving for variable 'x'.

Reorder the terms:
16 + -4 + -3x + 10x + x2 = 4 + -10x + -4 + 10x

Combine like terms: 16 + -4 = 12
12 + -3x + 10x + x2 = 4 + -10x + -4 + 10x

Combine like terms: -3x + 10x = 7x
12 + 7x + x2 = 4 + -10x + -4 + 10x

Reorder the terms:
12 + 7x + x2 = 4 + -4 + -10x + 10x

Combine like terms: 4 + -4 = 0
12 + 7x + x2 = 0 + -10x + 10x
12 + 7x + x2 = -10x + 10x

Combine like terms: -10x + 10x = 0
12 + 7x + x2 = 0

Factor a trinomial.
(4 + x)(3 + x) = 0

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 '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3

Solution

x = {-4, -3}

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