3x-6=4x^2-7

Solution for 3x-6=4x^2-7 equation:

Simplifying
3x + -6 = 4x2 + -7

Reorder the terms:
-6 + 3x = 4x2 + -7

Reorder the terms:
-6 + 3x = -7 + 4x2

Solving
-6 + 3x = -7 + 4x2

Solving for variable 'x'.

Reorder the terms:
-6 + 7 + 3x + -4x2 = -7 + 4x2 + 7 + -4x2

Combine like terms: -6 + 7 = 1
1 + 3x + -4x2 = -7 + 4x2 + 7 + -4x2

Reorder the terms:
1 + 3x + -4x2 = -7 + 7 + 4x2 + -4x2

Combine like terms: -7 + 7 = 0
1 + 3x + -4x2 = 0 + 4x2 + -4x2
1 + 3x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
1 + 3x + -4x2 = 0

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

Subproblem 1
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
Subproblem 2
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
Solution
x = {1, -0.25}