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

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


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

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

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

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

Multiply (2 + x) * (-3 + x)
-18 + x = 4(2(-3 + x) + x(-3 + x))
-18 + x = 4((-3 * 2 + x * 2) + x(-3 + x))
-18 + x = 4((-6 + 2x) + x(-3 + x))
-18 + x = 4(-6 + 2x + (-3 * x + x * x))
-18 + x = 4(-6 + 2x + (-3x + x2))

Combine like terms: 2x + -3x = -1x
-18 + x = 4(-6 + -1x + x2)
-18 + x = (-6 * 4 + -1x * 4 + x2 * 4)
-18 + x = (-24 + -4x + 4x2)

Solving
-18 + x = -24 + -4x + 4x2

Solving for variable 'x'.

Reorder the terms:
-18 + 24 + x + 4x + -4x2 = -24 + -4x + 4x2 + 24 + 4x + -4x2

Combine like terms: -18 + 24 = 6
6 + x + 4x + -4x2 = -24 + -4x + 4x2 + 24 + 4x + -4x2

Combine like terms: x + 4x = 5x
6 + 5x + -4x2 = -24 + -4x + 4x2 + 24 + 4x + -4x2

Reorder the terms:
6 + 5x + -4x2 = -24 + 24 + -4x + 4x + 4x2 + -4x2

Combine like terms: -24 + 24 = 0
6 + 5x + -4x2 = 0 + -4x + 4x + 4x2 + -4x2
6 + 5x + -4x2 = -4x + 4x + 4x2 + -4x2

Combine like terms: -4x + 4x = 0
6 + 5x + -4x2 = 0 + 4x2 + -4x2
6 + 5x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
6 + 5x + -4x2 = 0

Factor a trinomial.
(2 + -1x)(3 + 4x) = 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 '(3 + 4x)' equal to zero and attempt to solve:

Simplifying
3 + 4x = 0

Solving
3 + 4x = 0

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

Add '-3' to each side of the equation.
3 + -3 + 4x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4x = 0 + -3
4x = 0 + -3

Combine like terms: 0 + -3 = -3
4x = -3

Divide each side by '4'.
x = -0.75

Simplifying
x = -0.75
Solution
x = {2, -0.75}

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