4*X*X-21*X+55=7*X+10

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Solution for 4*X*X-21*X+55=7*X+10 equation: 


Simplifying
4X * X + -21X + 55 = 7X + 10

Multiply X * X
4X2 + -21X + 55 = 7X + 10

Reorder the terms:
55 + -21X + 4X2 = 7X + 10

Reorder the terms:
55 + -21X + 4X2 = 10 + 7X

Solving
55 + -21X + 4X2 = 10 + 7X

Solving for variable 'X'.

Reorder the terms:
55 + -10 + -21X + -7X + 4X2 = 10 + 7X + -10 + -7X

Combine like terms: 55 + -10 = 45
45 + -21X + -7X + 4X2 = 10 + 7X + -10 + -7X

Combine like terms: -21X + -7X = -28X
45 + -28X + 4X2 = 10 + 7X + -10 + -7X

Reorder the terms:
45 + -28X + 4X2 = 10 + -10 + 7X + -7X

Combine like terms: 10 + -10 = 0
45 + -28X + 4X2 = 0 + 7X + -7X
45 + -28X + 4X2 = 7X + -7X

Combine like terms: 7X + -7X = 0
45 + -28X + 4X2 = 0

Factor a trinomial.
(5 + -2X)(9 + -2X) = 0


Subproblem 1
Set the factor '(5 + -2X)' equal to zero and attempt to solve:

Simplifying
5 + -2X = 0

Solving
5 + -2X = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2X = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2X = 0 + -5
-2X = 0 + -5

Combine like terms: 0 + -5 = -5
-2X = -5

Divide each side by '-2'.
X = 2.5

Simplifying
X = 2.5

Subproblem 2
Set the factor '(9 + -2X)' equal to zero and attempt to solve:

Simplifying
9 + -2X = 0

Solving
9 + -2X = 0

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

Add '-9' to each side of the equation.
9 + -9 + -2X = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2X = 0 + -9
-2X = 0 + -9

Combine like terms: 0 + -9 = -9
-2X = -9

Divide each side by '-2'.
X = 4.5

Simplifying
X = 4.5
Solution
X = {2.5, 4.5}

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