x^2=4x^2-25x-50

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Solution for x^2=4x^2-25x-50 equation: 


Simplifying
x2 = 4x2 + -25x + -50

Reorder the terms:
x2 = -50 + -25x + 4x2

Solving
x2 = -50 + -25x + 4x2

Solving for variable 'x'.

Reorder the terms:
50 + 25x + x2 + -4x2 = -50 + -25x + 4x2 + 50 + 25x + -4x2

Combine like terms: x2 + -4x2 = -3x2
50 + 25x + -3x2 = -50 + -25x + 4x2 + 50 + 25x + -4x2

Reorder the terms:
50 + 25x + -3x2 = -50 + 50 + -25x + 25x + 4x2 + -4x2

Combine like terms: -50 + 50 = 0
50 + 25x + -3x2 = 0 + -25x + 25x + 4x2 + -4x2
50 + 25x + -3x2 = -25x + 25x + 4x2 + -4x2

Combine like terms: -25x + 25x = 0
50 + 25x + -3x2 = 0 + 4x2 + -4x2
50 + 25x + -3x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
50 + 25x + -3x2 = 0

Factor a trinomial.
(10 + -1x)(5 + 3x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(5 + 3x)' equal to zero and attempt to solve:

Simplifying
5 + 3x = 0

Solving
5 + 3x = 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 + 3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 3x = 0 + -5
3x = 0 + -5

Combine like terms: 0 + -5 = -5
3x = -5

Divide each side by '3'.
x = -1.666666667

Simplifying
x = -1.666666667
Solution
x = {10, -1.666666667}

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