4x(x-3)+36=64-2(x+2)

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Solution for 4x(x-3)+36=64-2(x+2) equation: 


Simplifying
4x(x + -3) + 36 = 64 + -2(x + 2)

Reorder the terms:
4x(-3 + x) + 36 = 64 + -2(x + 2)
(-3 * 4x + x * 4x) + 36 = 64 + -2(x + 2)
(-12x + 4x2) + 36 = 64 + -2(x + 2)

Reorder the terms:
36 + -12x + 4x2 = 64 + -2(x + 2)

Reorder the terms:
36 + -12x + 4x2 = 64 + -2(2 + x)
36 + -12x + 4x2 = 64 + (2 * -2 + x * -2)
36 + -12x + 4x2 = 64 + (-4 + -2x)

Combine like terms: 64 + -4 = 60
36 + -12x + 4x2 = 60 + -2x

Solving
36 + -12x + 4x2 = 60 + -2x

Solving for variable 'x'.

Reorder the terms:
36 + -60 + -12x + 2x + 4x2 = 60 + -2x + -60 + 2x

Combine like terms: 36 + -60 = -24
-24 + -12x + 2x + 4x2 = 60 + -2x + -60 + 2x

Combine like terms: -12x + 2x = -10x
-24 + -10x + 4x2 = 60 + -2x + -60 + 2x

Reorder the terms:
-24 + -10x + 4x2 = 60 + -60 + -2x + 2x

Combine like terms: 60 + -60 = 0
-24 + -10x + 4x2 = 0 + -2x + 2x
-24 + -10x + 4x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
-24 + -10x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + -5x + 2x2) = 0

Factor a trinomial.
2((-3 + -2x)(4 + -1x)) = 0

Ignore the factor 2.

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 '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-1.5, 4}

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