3(2x^2-1)=-7x

Solution for 3(2x^2-1)=-7x equation:

Simplifying
3(2x2 + -1) = -7x

Reorder the terms:
3(-1 + 2x2) = -7x
(-1 * 3 + 2x2 * 3) = -7x
(-3 + 6x2) = -7x

Solving
-3 + 6x2 = -7x

Solving for variable 'x'.

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

Combine like terms: -7x + 7x = 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}