4x^2-10+13x-20=x^2

Solution for 4x^2-10+13x-20=x^2 equation:

Simplifying
4x2 + -10 + 13x + -20 = x2

Reorder the terms:
-10 + -20 + 13x + 4x2 = x2

Combine like terms: -10 + -20 = -30
-30 + 13x + 4x2 = x2

Solving
-30 + 13x + 4x2 = x2

Solving for variable 'x'.

Combine like terms: 4x2 + -1x2 = 3x2
-30 + 13x + 3x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-30 + 13x + 3x2 = 0

Factor a trinomial.
(-6 + -1x)(5 + -3x) = 0

Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6
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 = {-6, 1.666666667}