x^2+11x=4x-6

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Solution for x^2+11x=4x-6 equation:


Simplifying
x2 + 11x = 4x + -6

Reorder the terms:
11x + x2 = 4x + -6

Reorder the terms:
11x + x2 = -6 + 4x

Solving
11x + x2 = -6 + 4x

Solving for variable 'x'.

Reorder the terms:
6 + 11x + -4x + x2 = -6 + 4x + 6 + -4x

Combine like terms: 11x + -4x = 7x
6 + 7x + x2 = -6 + 4x + 6 + -4x

Reorder the terms:
6 + 7x + x2 = -6 + 6 + 4x + -4x

Combine like terms: -6 + 6 = 0
6 + 7x + x2 = 0 + 4x + -4x
6 + 7x + x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
6 + 7x + x2 = 0

Factor a trinomial.
(6 + x)(1 + x) = 0

Subproblem 1

Set the factor '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6

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 = {-6, -1}

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