4x^2+5=41x-5

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Solution for 4x^2+5=41x-5 equation:


Simplifying
4x2 + 5 = 41x + -5

Reorder the terms:
5 + 4x2 = 41x + -5

Reorder the terms:
5 + 4x2 = -5 + 41x

Solving
5 + 4x2 = -5 + 41x

Solving for variable 'x'.

Reorder the terms:
5 + 5 + -41x + 4x2 = -5 + 41x + 5 + -41x

Combine like terms: 5 + 5 = 10
10 + -41x + 4x2 = -5 + 41x + 5 + -41x

Reorder the terms:
10 + -41x + 4x2 = -5 + 5 + 41x + -41x

Combine like terms: -5 + 5 = 0
10 + -41x + 4x2 = 0 + 41x + -41x
10 + -41x + 4x2 = 41x + -41x

Combine like terms: 41x + -41x = 0
10 + -41x + 4x2 = 0

Factor a trinomial.
(1 + -4x)(10 + -1x) = 0


Subproblem 1
Set the factor '(1 + -4x)' equal to zero and attempt to solve:

Simplifying
1 + -4x = 0

Solving
1 + -4x = 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 + -4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4x = 0 + -1
-4x = 0 + -1

Combine like terms: 0 + -1 = -1
-4x = -1

Divide each side by '-4'.
x = 0.25

Simplifying
x = 0.25

Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {0.25, 10}

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