4x^2-9x+21=8x+6

Solution for 4x^2-9x+21=8x+6 equation:

Simplifying
4x2 + -9x + 21 = 8x + 6

Reorder the terms:
21 + -9x + 4x2 = 8x + 6

Reorder the terms:
21 + -9x + 4x2 = 6 + 8x

Solving
21 + -9x + 4x2 = 6 + 8x

Solving for variable 'x'.

Reorder the terms:
21 + -6 + -9x + -8x + 4x2 = 6 + 8x + -6 + -8x

Combine like terms: 21 + -6 = 15
15 + -9x + -8x + 4x2 = 6 + 8x + -6 + -8x

Combine like terms: -9x + -8x = -17x
15 + -17x + 4x2 = 6 + 8x + -6 + -8x

Reorder the terms:
15 + -17x + 4x2 = 6 + -6 + 8x + -8x

Combine like terms: 6 + -6 = 0
15 + -17x + 4x2 = 0 + 8x + -8x
15 + -17x + 4x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
15 + -17x + 4x2 = 0

Factor a trinomial.
(5 + -4x)(3 + -1x) = 0

Subproblem 1
Set the factor '(5 + -4x)' equal to zero and attempt to solve:

Simplifying
5 + -4x = 0

Solving
5 + -4x = 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 + -4x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4x = 0 + -5
-4x = 0 + -5

Combine like terms: 0 + -5 = -5
-4x = -5

Divide each side by '-4'.
x = 1.25

Simplifying
x = 1.25
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {1.25, 3}