8x^2=14x-6

Solution for 8x^2=14x-6 equation:

Simplifying
8x2 = 14x + -6

Reorder the terms:
8x2 = -6 + 14x

Solving
8x2 = -6 + 14x

Solving for variable 'x'.

Reorder the terms:
6 + -14x + 8x2 = -6 + 14x + 6 + -14x

Reorder the terms:
6 + -14x + 8x2 = -6 + 6 + 14x + -14x

Combine like terms: -6 + 6 = 0
6 + -14x + 8x2 = 0 + 14x + -14x
6 + -14x + 8x2 = 14x + -14x

Combine like terms: 14x + -14x = 0
6 + -14x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -7x + 4x2) = 0

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

Ignore the factor 2.
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 '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
Solution
x = {0.75, 1}