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

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

Simplifying
3(x2 + -4) + 7(x + -2) * x = 0

Reorder the terms:
3(-4 + x2) + 7(x + -2) * x = 0
(-4 * 3 + x2 * 3) + 7(x + -2) * x = 0
(-12 + 3x2) + 7(x + -2) * x = 0

Reorder the terms:
-12 + 3x2 + 7(-2 + x) * x = 0

Reorder the terms for easier multiplication:
-12 + 3x2 + 7x(-2 + x) = 0
-12 + 3x2 + (-2 * 7x + x * 7x) = 0
-12 + 3x2 + (-14x + 7x2) = 0

Reorder the terms:
-12 + -14x + 3x2 + 7x2 = 0

Combine like terms: 3x2 + 7x2 = 10x2
-12 + -14x + 10x2 = 0

Solving
-12 + -14x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + -7x + 5x2) = 0

Factor a trinomial.
2((-3 + -5x)(2 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + -5x)' equal to zero and attempt to solve:

Simplifying
-3 + -5x = 0

Solving
-3 + -5x = 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 + -5x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -5x = 0 + 3
-5x = 0 + 3

Combine like terms: 0 + 3 = 3
-5x = 3

Divide each side by '-5'.
x = -0.6

Simplifying
x = -0.6
Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-0.6, 2}