4x^2-14x=4+5x-x^2

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Solution for 4x^2-14x=4+5x-x^2 equation: 


Simplifying
4x2 + -14x = 4 + 5x + -1x2

Reorder the terms:
-14x + 4x2 = 4 + 5x + -1x2

Solving
-14x + 4x2 = 4 + 5x + -1x2

Solving for variable 'x'.

Reorder the terms:
-4 + -14x + -5x + 4x2 + x2 = 4 + 5x + -1x2 + -4 + -5x + x2

Combine like terms: -14x + -5x = -19x
-4 + -19x + 4x2 + x2 = 4 + 5x + -1x2 + -4 + -5x + x2

Combine like terms: 4x2 + x2 = 5x2
-4 + -19x + 5x2 = 4 + 5x + -1x2 + -4 + -5x + x2

Reorder the terms:
-4 + -19x + 5x2 = 4 + -4 + 5x + -5x + -1x2 + x2

Combine like terms: 4 + -4 = 0
-4 + -19x + 5x2 = 0 + 5x + -5x + -1x2 + x2
-4 + -19x + 5x2 = 5x + -5x + -1x2 + x2

Combine like terms: 5x + -5x = 0
-4 + -19x + 5x2 = 0 + -1x2 + x2
-4 + -19x + 5x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-4 + -19x + 5x2 = 0

Factor a trinomial.
(-1 + -5x)(4 + -1x) = 0


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

Simplifying
-1 + -5x = 0

Solving
-1 + -5x = 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 + -5x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -5x = 0 + 1
-5x = 0 + 1

Combine like terms: 0 + 1 = 1
-5x = 1

Divide each side by '-5'.
x = -0.2

Simplifying
x = -0.2

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 = {-0.2, 4}

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