5-20x^2=5(1-2x)(1+3x)

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Solution for 5-20x^2=5(1-2x)(1+3x) equation: 


Simplifying
5 + -20x2 = 5(1 + -2x)(1 + 3x)

Multiply (1 + -2x) * (1 + 3x)
5 + -20x2 = 5(1(1 + 3x) + -2x * (1 + 3x))
5 + -20x2 = 5((1 * 1 + 3x * 1) + -2x * (1 + 3x))
5 + -20x2 = 5((1 + 3x) + -2x * (1 + 3x))
5 + -20x2 = 5(1 + 3x + (1 * -2x + 3x * -2x))
5 + -20x2 = 5(1 + 3x + (-2x + -6x2))

Combine like terms: 3x + -2x = 1x
5 + -20x2 = 5(1 + 1x + -6x2)
5 + -20x2 = (1 * 5 + 1x * 5 + -6x2 * 5)
5 + -20x2 = (5 + 5x + -30x2)

Add '-5' to each side of the equation.
5 + -5 + -20x2 = 5 + 5x + -5 + -30x2

Combine like terms: 5 + -5 = 0
0 + -20x2 = 5 + 5x + -5 + -30x2
-20x2 = 5 + 5x + -5 + -30x2

Reorder the terms:
-20x2 = 5 + -5 + 5x + -30x2

Combine like terms: 5 + -5 = 0
-20x2 = 0 + 5x + -30x2
-20x2 = 5x + -30x2

Solving
-20x2 = 5x + -30x2

Solving for variable 'x'.

Reorder the terms:
-5x + -20x2 + 30x2 = 5x + -30x2 + -5x + 30x2

Combine like terms: -20x2 + 30x2 = 10x2
-5x + 10x2 = 5x + -30x2 + -5x + 30x2

Reorder the terms:
-5x + 10x2 = 5x + -5x + -30x2 + 30x2

Combine like terms: 5x + -5x = 0
-5x + 10x2 = 0 + -30x2 + 30x2
-5x + 10x2 = -30x2 + 30x2

Combine like terms: -30x2 + 30x2 = 0
-5x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '5x'.
5x(-1 + 2x) = 0

Ignore the factor 5.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

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

Simplifying
-1 + 2x = 0

Solving
-1 + 2x = 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 + 2x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2x = 0 + 1
2x = 0 + 1

Combine like terms: 0 + 1 = 1
2x = 1

Divide each side by '2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {0, 0.5}

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