5x-3x(x-5)=-7+4x+12

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Solution for 5x-3x(x-5)=-7+4x+12 equation: 


Simplifying
5x + -3x(x + -5) = -7 + 4x + 12

Reorder the terms:
5x + -3x(-5 + x) = -7 + 4x + 12
5x + (-5 * -3x + x * -3x) = -7 + 4x + 12
5x + (15x + -3x2) = -7 + 4x + 12

Combine like terms: 5x + 15x = 20x
20x + -3x2 = -7 + 4x + 12

Reorder the terms:
20x + -3x2 = -7 + 12 + 4x

Combine like terms: -7 + 12 = 5
20x + -3x2 = 5 + 4x

Solving
20x + -3x2 = 5 + 4x

Solving for variable 'x'.

Reorder the terms:
-5 + 20x + -4x + -3x2 = 5 + 4x + -5 + -4x

Combine like terms: 20x + -4x = 16x
-5 + 16x + -3x2 = 5 + 4x + -5 + -4x

Reorder the terms:
-5 + 16x + -3x2 = 5 + -5 + 4x + -4x

Combine like terms: 5 + -5 = 0
-5 + 16x + -3x2 = 0 + 4x + -4x
-5 + 16x + -3x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-5 + 16x + -3x2 = 0

Factor a trinomial.
(-5 + x)(1 + -3x) = 0


Subproblem 1
Set the factor '(-5 + x)' equal to zero and attempt to solve:

Simplifying
-5 + x = 0

Solving
-5 + x = 0

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

Add '5' to each side of the equation.
-5 + 5 + x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + x = 0 + 5
x = 0 + 5

Combine like terms: 0 + 5 = 5
x = 5

Simplifying
x = 5

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

Simplifying
1 + -3x = 0

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

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

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

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Solution
x = {5, 0.3333333333}

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