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

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


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

Reorder the terms:
(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 + x2) = 0

Factor a trinomial.
6((-1 + -1x)(2 + -1x)) = 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 + -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 = {-1, 2}

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