4x^2-11x=8x+5

Solution for 4x^2-11x=8x+5 equation:

Simplifying
4x2 + -11x = 8x + 5

Reorder the terms:
-11x + 4x2 = 8x + 5

Reorder the terms:
-11x + 4x2 = 5 + 8x

Solving
-11x + 4x2 = 5 + 8x

Solving for variable 'x'.

Reorder the terms:
-5 + -11x + -8x + 4x2 = 5 + 8x + -5 + -8x

Combine like terms: -11x + -8x = -19x
-5 + -19x + 4x2 = 5 + 8x + -5 + -8x

Reorder the terms:
-5 + -19x + 4x2 = 5 + -5 + 8x + -8x

Combine like terms: 5 + -5 = 0
-5 + -19x + 4x2 = 0 + 8x + -8x
-5 + -19x + 4x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-5 + -19x + 4x2 = 0

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

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

Simplifying
-1 + -4x = 0

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

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

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

Divide each side by '-4'.
x = -0.25

Simplifying
x = -0.25
Subproblem 2
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
Solution
x = {-0.25, 5}