4x^2+35x+54=2x^2+21x+30

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Solution for 4x^2+35x+54=2x^2+21x+30 equation: 


Simplifying
4x2 + 35x + 54 = 2x2 + 21x + 30

Reorder the terms:
54 + 35x + 4x2 = 2x2 + 21x + 30

Reorder the terms:
54 + 35x + 4x2 = 30 + 21x + 2x2

Solving
54 + 35x + 4x2 = 30 + 21x + 2x2

Solving for variable 'x'.

Reorder the terms:
54 + -30 + 35x + -21x + 4x2 + -2x2 = 30 + 21x + 2x2 + -30 + -21x + -2x2

Combine like terms: 54 + -30 = 24
24 + 35x + -21x + 4x2 + -2x2 = 30 + 21x + 2x2 + -30 + -21x + -2x2

Combine like terms: 35x + -21x = 14x
24 + 14x + 4x2 + -2x2 = 30 + 21x + 2x2 + -30 + -21x + -2x2

Combine like terms: 4x2 + -2x2 = 2x2
24 + 14x + 2x2 = 30 + 21x + 2x2 + -30 + -21x + -2x2

Reorder the terms:
24 + 14x + 2x2 = 30 + -30 + 21x + -21x + 2x2 + -2x2

Combine like terms: 30 + -30 = 0
24 + 14x + 2x2 = 0 + 21x + -21x + 2x2 + -2x2
24 + 14x + 2x2 = 21x + -21x + 2x2 + -2x2

Combine like terms: 21x + -21x = 0
24 + 14x + 2x2 = 0 + 2x2 + -2x2
24 + 14x + 2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
24 + 14x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(12 + 7x + x2) = 0

Factor a trinomial.
2((4 + x)(3 + x)) = 0

Ignore the factor 2.

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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