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

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


Simplifying
3(2x2 + 3x) = 4(2x + 3)

Reorder the terms:
3(3x + 2x2) = 4(2x + 3)
(3x * 3 + 2x2 * 3) = 4(2x + 3)
(9x + 6x2) = 4(2x + 3)

Reorder the terms:
9x + 6x2 = 4(3 + 2x)
9x + 6x2 = (3 * 4 + 2x * 4)
9x + 6x2 = (12 + 8x)

Solving
9x + 6x2 = 12 + 8x

Solving for variable 'x'.

Reorder the terms:
-12 + 9x + -8x + 6x2 = 12 + 8x + -12 + -8x

Combine like terms: 9x + -8x = 1x
-12 + 1x + 6x2 = 12 + 8x + -12 + -8x

Reorder the terms:
-12 + 1x + 6x2 = 12 + -12 + 8x + -8x

Combine like terms: 12 + -12 = 0
-12 + 1x + 6x2 = 0 + 8x + -8x
-12 + 1x + 6x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-12 + 1x + 6x2 = 0

Factor a trinomial.
(-3 + -2x)(4 + -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 '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3x = 0 + -4

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

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

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333
Solution
x = {-1.5, 1.333333333}

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