4x^2-9x+10=8x+6

Solution for 4x^2-9x+10=8x+6 equation:

Simplifying
4x2 + -9x + 10 = 8x + 6

Reorder the terms:
10 + -9x + 4x2 = 8x + 6

Reorder the terms:
10 + -9x + 4x2 = 6 + 8x

Solving
10 + -9x + 4x2 = 6 + 8x

Solving for variable 'x'.

Reorder the terms:
10 + -6 + -9x + -8x + 4x2 = 6 + 8x + -6 + -8x

Combine like terms: 10 + -6 = 4
4 + -9x + -8x + 4x2 = 6 + 8x + -6 + -8x

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

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

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

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

Factor a trinomial.
(1 + -4x)(4 + -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 '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

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

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

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {0.25, 4}