4x^2-13x+11=-2x+5

Solution for 4x^2-13x+11=-2x+5 equation:

Simplifying
4x2 + -13x + 11 = -2x + 5

Reorder the terms:
11 + -13x + 4x2 = -2x + 5

Reorder the terms:
11 + -13x + 4x2 = 5 + -2x

Solving
11 + -13x + 4x2 = 5 + -2x

Solving for variable 'x'.

Reorder the terms:
11 + -5 + -13x + 2x + 4x2 = 5 + -2x + -5 + 2x

Combine like terms: 11 + -5 = 6
6 + -13x + 2x + 4x2 = 5 + -2x + -5 + 2x

Combine like terms: -13x + 2x = -11x
6 + -11x + 4x2 = 5 + -2x + -5 + 2x

Reorder the terms:
6 + -11x + 4x2 = 5 + -5 + -2x + 2x

Combine like terms: 5 + -5 = 0
6 + -11x + 4x2 = 0 + -2x + 2x
6 + -11x + 4x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
6 + -11x + 4x2 = 0

Factor a trinomial.
(3 + -4x)(2 + -1x) = 0

Subproblem 1
Set the factor '(3 + -4x)' equal to zero and attempt to solve:

Simplifying
3 + -4x = 0

Solving
3 + -4x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -4x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4x = 0 + -3
-4x = 0 + -3

Combine like terms: 0 + -3 = -3
-4x = -3

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75
Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {0.75, 2}