-2x(2x-3)+9=-4x+15

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Solution for -2x(2x-3)+9=-4x+15 equation: 


Simplifying
-2x(2x + -3) + 9 = -4x + 15

Reorder the terms:
-2x(-3 + 2x) + 9 = -4x + 15
(-3 * -2x + 2x * -2x) + 9 = -4x + 15
(6x + -4x2) + 9 = -4x + 15

Reorder the terms:
9 + 6x + -4x2 = -4x + 15

Reorder the terms:
9 + 6x + -4x2 = 15 + -4x

Solving
9 + 6x + -4x2 = 15 + -4x

Solving for variable 'x'.

Reorder the terms:
9 + -15 + 6x + 4x + -4x2 = 15 + -4x + -15 + 4x

Combine like terms: 9 + -15 = -6
-6 + 6x + 4x + -4x2 = 15 + -4x + -15 + 4x

Combine like terms: 6x + 4x = 10x
-6 + 10x + -4x2 = 15 + -4x + -15 + 4x

Reorder the terms:
-6 + 10x + -4x2 = 15 + -15 + -4x + 4x

Combine like terms: 15 + -15 = 0
-6 + 10x + -4x2 = 0 + -4x + 4x
-6 + 10x + -4x2 = -4x + 4x

Combine like terms: -4x + 4x = 0
-6 + 10x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 5x + -2x2) = 0

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

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
Solution
x = {1.5, 1}

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