6x(2x+3)-4(x-9)=2x+45

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Solution for 6x(2x+3)-4(x-9)=2x+45 equation: 


Simplifying
6x(2x + 3) + -4(x + -9) = 2x + 45

Reorder the terms:
6x(3 + 2x) + -4(x + -9) = 2x + 45
(3 * 6x + 2x * 6x) + -4(x + -9) = 2x + 45
(18x + 12x2) + -4(x + -9) = 2x + 45

Reorder the terms:
18x + 12x2 + -4(-9 + x) = 2x + 45
18x + 12x2 + (-9 * -4 + x * -4) = 2x + 45
18x + 12x2 + (36 + -4x) = 2x + 45

Reorder the terms:
36 + 18x + -4x + 12x2 = 2x + 45

Combine like terms: 18x + -4x = 14x
36 + 14x + 12x2 = 2x + 45

Reorder the terms:
36 + 14x + 12x2 = 45 + 2x

Solving
36 + 14x + 12x2 = 45 + 2x

Solving for variable 'x'.

Reorder the terms:
36 + -45 + 14x + -2x + 12x2 = 45 + 2x + -45 + -2x

Combine like terms: 36 + -45 = -9
-9 + 14x + -2x + 12x2 = 45 + 2x + -45 + -2x

Combine like terms: 14x + -2x = 12x
-9 + 12x + 12x2 = 45 + 2x + -45 + -2x

Reorder the terms:
-9 + 12x + 12x2 = 45 + -45 + 2x + -2x

Combine like terms: 45 + -45 = 0
-9 + 12x + 12x2 = 0 + 2x + -2x
-9 + 12x + 12x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-9 + 12x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-3 + 4x + 4x2) = 0

Factor a trinomial.
3((-3 + -2x)(1 + -2x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-3 + -2x)' equal to zero and attempt to solve:

Simplifying
-3 + -2x = 0

Solving
-3 + -2x = 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 + -2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2x = 0 + 3
-2x = 0 + 3

Combine like terms: 0 + 3 = 3
-2x = 3

Divide each side by '-2'.
x = -1.5

Simplifying
x = -1.5

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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {-1.5, 0.5}

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