4x^2-7x+21=9x+6

Solution for 4x^2-7x+21=9x+6 equation:

Simplifying
4x2 + -7x + 21 = 9x + 6

Reorder the terms:
21 + -7x + 4x2 = 9x + 6

Reorder the terms:
21 + -7x + 4x2 = 6 + 9x

Solving
21 + -7x + 4x2 = 6 + 9x

Solving for variable 'x'.

Reorder the terms:
21 + -6 + -7x + -9x + 4x2 = 6 + 9x + -6 + -9x

Combine like terms: 21 + -6 = 15
15 + -7x + -9x + 4x2 = 6 + 9x + -6 + -9x

Combine like terms: -7x + -9x = -16x
15 + -16x + 4x2 = 6 + 9x + -6 + -9x

Reorder the terms:
15 + -16x + 4x2 = 6 + -6 + 9x + -9x

Combine like terms: 6 + -6 = 0
15 + -16x + 4x2 = 0 + 9x + -9x
15 + -16x + 4x2 = 9x + -9x

Combine like terms: 9x + -9x = 0
15 + -16x + 4x2 = 0

Factor a trinomial.
(3 + -2x)(5 + -2x) = 0

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

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Subproblem 2
Set the factor '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 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 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {1.5, 2.5}