3x(x-5)-2x(x+4)=-90

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Solution for 3x(x-5)-2x(x+4)=-90 equation: 


Simplifying
3x(x + -5) + -2x(x + 4) = -90

Reorder the terms:
3x(-5 + x) + -2x(x + 4) = -90
(-5 * 3x + x * 3x) + -2x(x + 4) = -90
(-15x + 3x2) + -2x(x + 4) = -90

Reorder the terms:
-15x + 3x2 + -2x(4 + x) = -90
-15x + 3x2 + (4 * -2x + x * -2x) = -90
-15x + 3x2 + (-8x + -2x2) = -90

Reorder the terms:
-15x + -8x + 3x2 + -2x2 = -90

Combine like terms: -15x + -8x = -23x
-23x + 3x2 + -2x2 = -90

Combine like terms: 3x2 + -2x2 = 1x2
-23x + 1x2 = -90

Solving
-23x + 1x2 = -90

Solving for variable 'x'.

Reorder the terms:
90 + -23x + 1x2 = -90 + 90

Combine like terms: -90 + 90 = 0
90 + -23x + 1x2 = 0

Factor a trinomial.
(5 + -1x)(18 + -1x) = 0


Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5

Subproblem 2
Set the factor '(18 + -1x)' equal to zero and attempt to solve:

Simplifying
18 + -1x = 0

Solving
18 + -1x = 0

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

Add '-18' to each side of the equation.
18 + -18 + -1x = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -1x = 0 + -18
-1x = 0 + -18

Combine like terms: 0 + -18 = -18
-1x = -18

Divide each side by '-1'.
x = 18

Simplifying
x = 18
Solution
x = {5, 18}

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