3(2x^2-4)-4(x+2)=7x-10

Solution for 3(2x^2-4)-4(x+2)=7x-10 equation:

Simplifying
3(2x2 + -4) + -4(x + 2) = 7x + -10

Reorder the terms:
3(-4 + 2x2) + -4(x + 2) = 7x + -10
(-4 * 3 + 2x2 * 3) + -4(x + 2) = 7x + -10
(-12 + 6x2) + -4(x + 2) = 7x + -10

Reorder the terms:
-12 + 6x2 + -4(2 + x) = 7x + -10
-12 + 6x2 + (2 * -4 + x * -4) = 7x + -10
-12 + 6x2 + (-8 + -4x) = 7x + -10

Reorder the terms:
-12 + -8 + -4x + 6x2 = 7x + -10

Combine like terms: -12 + -8 = -20
-20 + -4x + 6x2 = 7x + -10

Reorder the terms:
-20 + -4x + 6x2 = -10 + 7x

Solving
-20 + -4x + 6x2 = -10 + 7x

Solving for variable 'x'.

Reorder the terms:
-20 + 10 + -4x + -7x + 6x2 = -10 + 7x + 10 + -7x

Combine like terms: -20 + 10 = -10
-10 + -4x + -7x + 6x2 = -10 + 7x + 10 + -7x

Combine like terms: -4x + -7x = -11x
-10 + -11x + 6x2 = -10 + 7x + 10 + -7x

Reorder the terms:
-10 + -11x + 6x2 = -10 + 10 + 7x + -7x

Combine like terms: -10 + 10 = 0
-10 + -11x + 6x2 = 0 + 7x + -7x
-10 + -11x + 6x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
-10 + -11x + 6x2 = 0

Factor a trinomial.
(-2 + -3x)(5 + -2x) = 0

Subproblem 1
Set the factor '(-2 + -3x)' equal to zero and attempt to solve:

Simplifying
-2 + -3x = 0

Solving
-2 + -3x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -3x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3x = 0 + 2
-3x = 0 + 2

Combine like terms: 0 + 2 = 2
-3x = 2

Divide each side by '-3'.
x = -0.6666666667

Simplifying
x = -0.6666666667
Subproblem 2
Set the factor '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {-0.6666666667, 2.5}