3(2x^2+x-6)=4(x^2-x-6)

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Solution for 3(2x^2+x-6)=4(x^2-x-6) equation: 


Simplifying
3(2x2 + x + -6) = 4(x2 + -1x + -6)

Reorder the terms:
3(-6 + x + 2x2) = 4(x2 + -1x + -6)
(-6 * 3 + x * 3 + 2x2 * 3) = 4(x2 + -1x + -6)
(-18 + 3x + 6x2) = 4(x2 + -1x + -6)

Reorder the terms:
-18 + 3x + 6x2 = 4(-6 + -1x + x2)
-18 + 3x + 6x2 = (-6 * 4 + -1x * 4 + x2 * 4)
-18 + 3x + 6x2 = (-24 + -4x + 4x2)

Solving
-18 + 3x + 6x2 = -24 + -4x + 4x2

Solving for variable 'x'.

Reorder the terms:
-18 + 24 + 3x + 4x + 6x2 + -4x2 = -24 + -4x + 4x2 + 24 + 4x + -4x2

Combine like terms: -18 + 24 = 6
6 + 3x + 4x + 6x2 + -4x2 = -24 + -4x + 4x2 + 24 + 4x + -4x2

Combine like terms: 3x + 4x = 7x
6 + 7x + 6x2 + -4x2 = -24 + -4x + 4x2 + 24 + 4x + -4x2

Combine like terms: 6x2 + -4x2 = 2x2
6 + 7x + 2x2 = -24 + -4x + 4x2 + 24 + 4x + -4x2

Reorder the terms:
6 + 7x + 2x2 = -24 + 24 + -4x + 4x + 4x2 + -4x2

Combine like terms: -24 + 24 = 0
6 + 7x + 2x2 = 0 + -4x + 4x + 4x2 + -4x2
6 + 7x + 2x2 = -4x + 4x + 4x2 + -4x2

Combine like terms: -4x + 4x = 0
6 + 7x + 2x2 = 0 + 4x2 + -4x2
6 + 7x + 2x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
6 + 7x + 2x2 = 0

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


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

Simplifying
2 + x = 0

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

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

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

Simplifying
x = -2

Subproblem 2
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
Solution
x = {-2, -1.5}

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