4x(x-20)=6x+138

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Solution for 4x(x-20)=6x+138 equation: 


Simplifying
4x(x + -20) = 6x + 138

Reorder the terms:
4x(-20 + x) = 6x + 138
(-20 * 4x + x * 4x) = 6x + 138
(-80x + 4x2) = 6x + 138

Reorder the terms:
-80x + 4x2 = 138 + 6x

Solving
-80x + 4x2 = 138 + 6x

Solving for variable 'x'.

Reorder the terms:
-138 + -80x + -6x + 4x2 = 138 + 6x + -138 + -6x

Combine like terms: -80x + -6x = -86x
-138 + -86x + 4x2 = 138 + 6x + -138 + -6x

Reorder the terms:
-138 + -86x + 4x2 = 138 + -138 + 6x + -6x

Combine like terms: 138 + -138 = 0
-138 + -86x + 4x2 = 0 + 6x + -6x
-138 + -86x + 4x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-138 + -86x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-69 + -43x + 2x2) = 0

Factor a trinomial.
2((-3 + -2x)(23 + -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 '(23 + -1x)' equal to zero and attempt to solve:

Simplifying
23 + -1x = 0

Solving
23 + -1x = 0

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

Add '-23' to each side of the equation.
23 + -23 + -1x = 0 + -23

Combine like terms: 23 + -23 = 0
0 + -1x = 0 + -23
-1x = 0 + -23

Combine like terms: 0 + -23 = -23
-1x = -23

Divide each side by '-1'.
x = 23

Simplifying
x = 23
Solution
x = {-1.5, 23}

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