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

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

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

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

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

Multiply (3 + x) * (-3 + x)
2(3(-3 + x) + x(-3 + x)) = 5x
2((-3 * 3 + x * 3) + x(-3 + x)) = 5x
2((-9 + 3x) + x(-3 + x)) = 5x
2(-9 + 3x + (-3 * x + x * x)) = 5x
2(-9 + 3x + (-3x + x2)) = 5x

Combine like terms: 3x + -3x = 0
2(-9 + 0 + x2) = 5x
2(-9 + x2) = 5x
(-9 * 2 + x2 * 2) = 5x
(-18 + 2x2) = 5x

Solving
-18 + 2x2 = 5x

Solving for variable 'x'.

Reorder the terms:
-18 + -5x + 2x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-18 + -5x + 2x2 = 0

Factor a trinomial.
(-2 + -1x)(9 + -2x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(9 + -2x)' equal to zero and attempt to solve:

Simplifying
9 + -2x = 0

Solving
9 + -2x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -2x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2x = 0 + -9
-2x = 0 + -9

Combine like terms: 0 + -9 = -9
-2x = -9

Divide each side by '-2'.
x = 4.5

Simplifying
x = 4.5
Solution
x = {-2, 4.5}