4x(x-5)=-7+3(x^2)-12x

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Solution for 4x(x-5)=-7+3(x^2)-12x equation: 


Simplifying
4x(x + -5) = -7 + 3(x2) + -12x

Reorder the terms:
4x(-5 + x) = -7 + 3(x2) + -12x
(-5 * 4x + x * 4x) = -7 + 3(x2) + -12x
(-20x + 4x2) = -7 + 3(x2) + -12x

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

Solving
-20x + 4x2 = -7 + -12x + 3x2

Solving for variable 'x'.

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

Combine like terms: -20x + 12x = -8x
7 + -8x + 4x2 + -3x2 = -7 + -12x + 3x2 + 7 + 12x + -3x2

Combine like terms: 4x2 + -3x2 = 1x2
7 + -8x + 1x2 = -7 + -12x + 3x2 + 7 + 12x + -3x2

Reorder the terms:
7 + -8x + 1x2 = -7 + 7 + -12x + 12x + 3x2 + -3x2

Combine like terms: -7 + 7 = 0
7 + -8x + 1x2 = 0 + -12x + 12x + 3x2 + -3x2
7 + -8x + 1x2 = -12x + 12x + 3x2 + -3x2

Combine like terms: -12x + 12x = 0
7 + -8x + 1x2 = 0 + 3x2 + -3x2
7 + -8x + 1x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
7 + -8x + 1x2 = 0

Factor a trinomial.
(1 + -1x)(7 + -1x) = 0


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

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1

Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {1, 7}

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