4x^2-10x=x^2+x+4

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Solution for 4x^2-10x=x^2+x+4 equation: 


Simplifying
4x2 + -10x = x2 + x + 4

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

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

Solving
-10x + 4x2 = 4 + x + x2

Solving for variable 'x'.

Reorder the terms:
-4 + -10x + -1x + 4x2 + -1x2 = 4 + x + x2 + -4 + -1x + -1x2

Combine like terms: -10x + -1x = -11x
-4 + -11x + 4x2 + -1x2 = 4 + x + x2 + -4 + -1x + -1x2

Combine like terms: 4x2 + -1x2 = 3x2
-4 + -11x + 3x2 = 4 + x + x2 + -4 + -1x + -1x2

Reorder the terms:
-4 + -11x + 3x2 = 4 + -4 + x + -1x + x2 + -1x2

Combine like terms: 4 + -4 = 0
-4 + -11x + 3x2 = 0 + x + -1x + x2 + -1x2
-4 + -11x + 3x2 = x + -1x + x2 + -1x2

Combine like terms: x + -1x = 0
-4 + -11x + 3x2 = 0 + x2 + -1x2
-4 + -11x + 3x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-4 + -11x + 3x2 = 0

Factor a trinomial.
(-1 + -3x)(4 + -1x) = 0


Subproblem 1
Set the factor '(-1 + -3x)' equal to zero and attempt to solve:

Simplifying
-1 + -3x = 0

Solving
-1 + -3x = 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 + -3x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3x = 0 + 1
-3x = 0 + 1

Combine like terms: 0 + 1 = 1
-3x = 1

Divide each side by '-3'.
x = -0.3333333333

Simplifying
x = -0.3333333333

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

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

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

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

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-0.3333333333, 4}

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