x^2+14x+21=4x-3

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Solution for x^2+14x+21=4x-3 equation:


Simplifying
x2 + 14x + 21 = 4x + -3

Reorder the terms:
21 + 14x + x2 = 4x + -3

Reorder the terms:
21 + 14x + x2 = -3 + 4x

Solving
21 + 14x + x2 = -3 + 4x

Solving for variable 'x'.

Reorder the terms:
21 + 3 + 14x + -4x + x2 = -3 + 4x + 3 + -4x

Combine like terms: 21 + 3 = 24
24 + 14x + -4x + x2 = -3 + 4x + 3 + -4x

Combine like terms: 14x + -4x = 10x
24 + 10x + x2 = -3 + 4x + 3 + -4x

Reorder the terms:
24 + 10x + x2 = -3 + 3 + 4x + -4x

Combine like terms: -3 + 3 = 0
24 + 10x + x2 = 0 + 4x + -4x
24 + 10x + x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
24 + 10x + x2 = 0

Factor a trinomial.
(6 + x)(4 + 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 '(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 = {-6, -4}

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