4x^2-5=x(x-14)

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

Simplifying
4x2 + -5 = x(x + -14)

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

Reorder the terms:
-5 + 4x2 = x(-14 + x)
-5 + 4x2 = (-14 * x + x * x)
-5 + 4x2 = (-14x + x2)

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

Solving for variable 'x'.

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

Combine like terms: 4x2 + -1x2 = 3x2
-5 + 14x + 3x2 = -14x + x2 + 14x + -1x2

Reorder the terms:
-5 + 14x + 3x2 = -14x + 14x + x2 + -1x2

Combine like terms: -14x + 14x = 0
-5 + 14x + 3x2 = 0 + x2 + -1x2
-5 + 14x + 3x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-5 + 14x + 3x2 = 0

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

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

Simplifying
-5 + -1x = 0

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

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

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

Divide each side by '-1'.
x = -5

Simplifying
x = -5
Subproblem 2
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
Solution
x = {-5, 0.3333333333}