(3x-4)(2x+5)=18

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Solution for (3x-4)(2x+5)=18 equation: 


Simplifying
(3x + -4)(2x + 5) = 18

Reorder the terms:
(-4 + 3x)(2x + 5) = 18

Reorder the terms:
(-4 + 3x)(5 + 2x) = 18

Multiply (-4 + 3x) * (5 + 2x)
(-4(5 + 2x) + 3x * (5 + 2x)) = 18
((5 * -4 + 2x * -4) + 3x * (5 + 2x)) = 18
((-20 + -8x) + 3x * (5 + 2x)) = 18
(-20 + -8x + (5 * 3x + 2x * 3x)) = 18
(-20 + -8x + (15x + 6x2)) = 18

Combine like terms: -8x + 15x = 7x
(-20 + 7x + 6x2) = 18

Solving
-20 + 7x + 6x2 = 18

Solving for variable 'x'.

Reorder the terms:
-20 + -18 + 7x + 6x2 = 18 + -18

Combine like terms: -20 + -18 = -38
-38 + 7x + 6x2 = 18 + -18

Combine like terms: 18 + -18 = 0
-38 + 7x + 6x2 = 0

Factor a trinomial.
(-19 + -6x)(2 + -1x) = 0


Subproblem 1
Set the factor '(-19 + -6x)' equal to zero and attempt to solve:

Simplifying
-19 + -6x = 0

Solving
-19 + -6x = 0

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

Add '19' to each side of the equation.
-19 + 19 + -6x = 0 + 19

Combine like terms: -19 + 19 = 0
0 + -6x = 0 + 19
-6x = 0 + 19

Combine like terms: 0 + 19 = 19
-6x = 19

Divide each side by '-6'.
x = -3.166666667

Simplifying
x = -3.166666667

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 = {-3.166666667, 2}

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