16x(x-3)-36(x-5)=4x^2-8x+60

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Solution for 16x(x-3)-36(x-5)=4x^2-8x+60 equation: 


Simplifying
16x(x + -3) + -36(x + -5) = 4x2 + -8x + 60

Reorder the terms:
16x(-3 + x) + -36(x + -5) = 4x2 + -8x + 60
(-3 * 16x + x * 16x) + -36(x + -5) = 4x2 + -8x + 60
(-48x + 16x2) + -36(x + -5) = 4x2 + -8x + 60

Reorder the terms:
-48x + 16x2 + -36(-5 + x) = 4x2 + -8x + 60
-48x + 16x2 + (-5 * -36 + x * -36) = 4x2 + -8x + 60
-48x + 16x2 + (180 + -36x) = 4x2 + -8x + 60

Reorder the terms:
180 + -48x + -36x + 16x2 = 4x2 + -8x + 60

Combine like terms: -48x + -36x = -84x
180 + -84x + 16x2 = 4x2 + -8x + 60

Reorder the terms:
180 + -84x + 16x2 = 60 + -8x + 4x2

Solving
180 + -84x + 16x2 = 60 + -8x + 4x2

Solving for variable 'x'.

Reorder the terms:
180 + -60 + -84x + 8x + 16x2 + -4x2 = 60 + -8x + 4x2 + -60 + 8x + -4x2

Combine like terms: 180 + -60 = 120
120 + -84x + 8x + 16x2 + -4x2 = 60 + -8x + 4x2 + -60 + 8x + -4x2

Combine like terms: -84x + 8x = -76x
120 + -76x + 16x2 + -4x2 = 60 + -8x + 4x2 + -60 + 8x + -4x2

Combine like terms: 16x2 + -4x2 = 12x2
120 + -76x + 12x2 = 60 + -8x + 4x2 + -60 + 8x + -4x2

Reorder the terms:
120 + -76x + 12x2 = 60 + -60 + -8x + 8x + 4x2 + -4x2

Combine like terms: 60 + -60 = 0
120 + -76x + 12x2 = 0 + -8x + 8x + 4x2 + -4x2
120 + -76x + 12x2 = -8x + 8x + 4x2 + -4x2

Combine like terms: -8x + 8x = 0
120 + -76x + 12x2 = 0 + 4x2 + -4x2
120 + -76x + 12x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
120 + -76x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(30 + -19x + 3x2) = 0

Factor a trinomial.
4((3 + -1x)(10 + -3x)) = 0

Ignore the factor 4.

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

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3

Subproblem 2
Set the factor '(10 + -3x)' equal to zero and attempt to solve:

Simplifying
10 + -3x = 0

Solving
10 + -3x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -3x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -3x = 0 + -10
-3x = 0 + -10

Combine like terms: 0 + -10 = -10
-3x = -10

Divide each side by '-3'.
x = 3.333333333

Simplifying
x = 3.333333333
Solution
x = {3, 3.333333333}

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