(5x^2+12x+7)-(x^2+2x+1)=

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Solution for (5x^2+12x+7)-(x^2+2x+1)= equation:


Simplifying
(5x2 + 12x + 7) + -1(x2 + 2x + 1) = 0

Reorder the terms:
(7 + 12x + 5x2) + -1(x2 + 2x + 1) = 0

Remove parenthesis around (7 + 12x + 5x2)
7 + 12x + 5x2 + -1(x2 + 2x + 1) = 0

Reorder the terms:
7 + 12x + 5x2 + -1(1 + 2x + x2) = 0
7 + 12x + 5x2 + (1 * -1 + 2x * -1 + x2 * -1) = 0
7 + 12x + 5x2 + (-1 + -2x + -1x2) = 0

Reorder the terms:
7 + -1 + 12x + -2x + 5x2 + -1x2 = 0

Combine like terms: 7 + -1 = 6
6 + 12x + -2x + 5x2 + -1x2 = 0

Combine like terms: 12x + -2x = 10x
6 + 10x + 5x2 + -1x2 = 0

Combine like terms: 5x2 + -1x2 = 4x2
6 + 10x + 4x2 = 0

Solving
6 + 10x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 5x + 2x2) = 0

Factor a trinomial.
2((3 + 2x)(1 + x)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 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 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Divide each side by '2'. x = -1.5 Simplifying x = -1.5

Subproblem 2

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

Solution

x = {-1.5, -1}

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