-4x(5x-1)=6(-2x-6)

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Solution for -4x(5x-1)=6(-2x-6) equation: 


Simplifying
-4x(5x + -1) = 6(-2x + -6)

Reorder the terms:
-4x(-1 + 5x) = 6(-2x + -6)
(-1 * -4x + 5x * -4x) = 6(-2x + -6)
(4x + -20x2) = 6(-2x + -6)

Reorder the terms:
4x + -20x2 = 6(-6 + -2x)
4x + -20x2 = (-6 * 6 + -2x * 6)
4x + -20x2 = (-36 + -12x)

Solving
4x + -20x2 = -36 + -12x

Solving for variable 'x'.

Reorder the terms:
36 + 4x + 12x + -20x2 = -36 + -12x + 36 + 12x

Combine like terms: 4x + 12x = 16x
36 + 16x + -20x2 = -36 + -12x + 36 + 12x

Reorder the terms:
36 + 16x + -20x2 = -36 + 36 + -12x + 12x

Combine like terms: -36 + 36 = 0
36 + 16x + -20x2 = 0 + -12x + 12x
36 + 16x + -20x2 = -12x + 12x

Combine like terms: -12x + 12x = 0
36 + 16x + -20x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(9 + 4x + -5x2) = 0

Factor a trinomial.
4((9 + -5x)(1 + x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(9 + -5x)' equal to zero and attempt to solve:

Simplifying
9 + -5x = 0

Solving
9 + -5x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -5x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -5x = 0 + -9
-5x = 0 + -9

Combine like terms: 0 + -9 = -9
-5x = -9

Divide each side by '-5'.
x = 1.8

Simplifying
x = 1.8

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

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Solution
x = {1.8, -1}

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