4x(2-x)=-3(2x+6)

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Solution for 4x(2-x)=-3(2x+6) equation: 


Simplifying
4x(2 + -1x) = -3(2x + 6)
(2 * 4x + -1x * 4x) = -3(2x + 6)
(8x + -4x2) = -3(2x + 6)

Reorder the terms:
8x + -4x2 = -3(6 + 2x)
8x + -4x2 = (6 * -3 + 2x * -3)
8x + -4x2 = (-18 + -6x)

Solving
8x + -4x2 = -18 + -6x

Solving for variable 'x'.

Reorder the terms:
18 + 8x + 6x + -4x2 = -18 + -6x + 18 + 6x

Combine like terms: 8x + 6x = 14x
18 + 14x + -4x2 = -18 + -6x + 18 + 6x

Reorder the terms:
18 + 14x + -4x2 = -18 + 18 + -6x + 6x

Combine like terms: -18 + 18 = 0
18 + 14x + -4x2 = 0 + -6x + 6x
18 + 14x + -4x2 = -6x + 6x

Combine like terms: -6x + 6x = 0
18 + 14x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + 7x + -2x2) = 0

Factor a trinomial.
2((9 + -2x)(1 + x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(9 + -2x)' equal to zero and attempt to solve:

Simplifying
9 + -2x = 0

Solving
9 + -2x = 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 + -2x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2x = 0 + -9
-2x = 0 + -9

Combine like terms: 0 + -9 = -9
-2x = -9

Divide each side by '-2'.
x = 4.5

Simplifying
x = 4.5

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 = {4.5, -1}

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