(4-3x)(2x+3)=5x

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Solution for (4-3x)(2x+3)=5x equation: 


Simplifying
(4 + -3x)(2x + 3) = 5x

Reorder the terms:
(4 + -3x)(3 + 2x) = 5x

Multiply (4 + -3x) * (3 + 2x)
(4(3 + 2x) + -3x * (3 + 2x)) = 5x
((3 * 4 + 2x * 4) + -3x * (3 + 2x)) = 5x
((12 + 8x) + -3x * (3 + 2x)) = 5x
(12 + 8x + (3 * -3x + 2x * -3x)) = 5x
(12 + 8x + (-9x + -6x2)) = 5x

Combine like terms: 8x + -9x = -1x
(12 + -1x + -6x2) = 5x

Solving
12 + -1x + -6x2 = 5x

Solving for variable 'x'.

Reorder the terms:
12 + -1x + -5x + -6x2 = 5x + -5x

Combine like terms: -1x + -5x = -6x
12 + -6x + -6x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
12 + -6x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(2 + -1x + -1x2) = 0

Factor a trinomial.
6((1 + -1x)(2 + x)) = 0

Ignore the factor 6.

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

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1

Subproblem 2
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
Solution
x = {1, -2}

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