3=6x^2-7x

Solution for 3=6x^2-7x equation:

Simplifying
3 = 6x2 + -7x

Reorder the terms:
3 = -7x + 6x2

Solving
3 = -7x + 6x2

Solving for variable 'x'.

Reorder the terms:
3 + 7x + -6x2 = -7x + 7x + 6x2 + -6x2

Combine like terms: -7x + 7x = 0
3 + 7x + -6x2 = 0 + 6x2 + -6x2
3 + 7x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
3 + 7x + -6x2 = 0

Factor a trinomial.
(3 + -2x)(1 + 3x) = 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 '(1 + 3x)' equal to zero and attempt to solve:

Simplifying
1 + 3x = 0

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

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

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

Divide each side by '3'.
x = -0.3333333333

Simplifying
x = -0.3333333333
Solution
x = {1.5, -0.3333333333}