4x^2+21x=6x-14

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Solution for 4x^2+21x=6x-14 equation: 


Simplifying
4x2 + 21x = 6x + -14

Reorder the terms:
21x + 4x2 = 6x + -14

Reorder the terms:
21x + 4x2 = -14 + 6x

Solving
21x + 4x2 = -14 + 6x

Solving for variable 'x'.

Reorder the terms:
14 + 21x + -6x + 4x2 = -14 + 6x + 14 + -6x

Combine like terms: 21x + -6x = 15x
14 + 15x + 4x2 = -14 + 6x + 14 + -6x

Reorder the terms:
14 + 15x + 4x2 = -14 + 14 + 6x + -6x

Combine like terms: -14 + 14 = 0
14 + 15x + 4x2 = 0 + 6x + -6x
14 + 15x + 4x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
14 + 15x + 4x2 = 0

Factor a trinomial.
(2 + x)(7 + 4x) = 0


Subproblem 1
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2

Subproblem 2
Set the factor '(7 + 4x)' equal to zero and attempt to solve:

Simplifying
7 + 4x = 0

Solving
7 + 4x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + 4x = 0 + -7

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

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

Divide each side by '4'.
x = -1.75

Simplifying
x = -1.75
Solution
x = {-2, -1.75}

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