2x(5-2x)=8x-12

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Solution for 2x(5-2x)=8x-12 equation: 


Simplifying
2x(5 + -2x) = 8x + -12
(5 * 2x + -2x * 2x) = 8x + -12
(10x + -4x2) = 8x + -12

Reorder the terms:
10x + -4x2 = -12 + 8x

Solving
10x + -4x2 = -12 + 8x

Solving for variable 'x'.

Reorder the terms:
12 + 10x + -8x + -4x2 = -12 + 8x + 12 + -8x

Combine like terms: 10x + -8x = 2x
12 + 2x + -4x2 = -12 + 8x + 12 + -8x

Reorder the terms:
12 + 2x + -4x2 = -12 + 12 + 8x + -8x

Combine like terms: -12 + 12 = 0
12 + 2x + -4x2 = 0 + 8x + -8x
12 + 2x + -4x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
12 + 2x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + x + -2x2) = 0

Factor a trinomial.
2((2 + -1x)(3 + 2x)) = 0

Ignore the factor 2.

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2

Subproblem 2
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
Solution
x = {2, -1.5}

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