4X^2+25X+21=2X^2+15X+13

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Solution for 4X^2+25X+21=2X^2+15X+13 equation: 


Simplifying
4X2 + 25X + 21 = 2X2 + 15X + 13

Reorder the terms:
21 + 25X + 4X2 = 2X2 + 15X + 13

Reorder the terms:
21 + 25X + 4X2 = 13 + 15X + 2X2

Solving
21 + 25X + 4X2 = 13 + 15X + 2X2

Solving for variable 'X'.

Reorder the terms:
21 + -13 + 25X + -15X + 4X2 + -2X2 = 13 + 15X + 2X2 + -13 + -15X + -2X2

Combine like terms: 21 + -13 = 8
8 + 25X + -15X + 4X2 + -2X2 = 13 + 15X + 2X2 + -13 + -15X + -2X2

Combine like terms: 25X + -15X = 10X
8 + 10X + 4X2 + -2X2 = 13 + 15X + 2X2 + -13 + -15X + -2X2

Combine like terms: 4X2 + -2X2 = 2X2
8 + 10X + 2X2 = 13 + 15X + 2X2 + -13 + -15X + -2X2

Reorder the terms:
8 + 10X + 2X2 = 13 + -13 + 15X + -15X + 2X2 + -2X2

Combine like terms: 13 + -13 = 0
8 + 10X + 2X2 = 0 + 15X + -15X + 2X2 + -2X2
8 + 10X + 2X2 = 15X + -15X + 2X2 + -2X2

Combine like terms: 15X + -15X = 0
8 + 10X + 2X2 = 0 + 2X2 + -2X2
8 + 10X + 2X2 = 2X2 + -2X2

Combine like terms: 2X2 + -2X2 = 0
8 + 10X + 2X2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + 5X + X2) = 0

Factor a trinomial.
2((4 + X)(1 + 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 '(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 = {-4, -1}

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