4x^2-20x=6(-5+x)

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Solution for 4x^2-20x=6(-5+x) equation: 


Simplifying
4x2 + -20x = 6(-5 + x)

Reorder the terms:
-20x + 4x2 = 6(-5 + x)
-20x + 4x2 = (-5 * 6 + x * 6)
-20x + 4x2 = (-30 + 6x)

Solving
-20x + 4x2 = -30 + 6x

Solving for variable 'x'.

Reorder the terms:
30 + -20x + -6x + 4x2 = -30 + 6x + 30 + -6x

Combine like terms: -20x + -6x = -26x
30 + -26x + 4x2 = -30 + 6x + 30 + -6x

Reorder the terms:
30 + -26x + 4x2 = -30 + 30 + 6x + -6x

Combine like terms: -30 + 30 = 0
30 + -26x + 4x2 = 0 + 6x + -6x
30 + -26x + 4x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
30 + -26x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(15 + -13x + 2x2) = 0

Factor a trinomial.
2((3 + -2x)(5 + -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 '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {1.5, 5}

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