5(2x-3)=9-4x^2

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Solution for 5(2x-3)=9-4x^2 equation: 


Simplifying
5(2x + -3) = 9 + -4x2

Reorder the terms:
5(-3 + 2x) = 9 + -4x2
(-3 * 5 + 2x * 5) = 9 + -4x2
(-15 + 10x) = 9 + -4x2

Solving
-15 + 10x = 9 + -4x2

Solving for variable 'x'.

Reorder the terms:
-15 + -9 + 10x + 4x2 = 9 + -4x2 + -9 + 4x2

Combine like terms: -15 + -9 = -24
-24 + 10x + 4x2 = 9 + -4x2 + -9 + 4x2

Reorder the terms:
-24 + 10x + 4x2 = 9 + -9 + -4x2 + 4x2

Combine like terms: 9 + -9 = 0
-24 + 10x + 4x2 = 0 + -4x2 + 4x2
-24 + 10x + 4x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
-24 + 10x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + 5x + 2x2) = 0

Factor a trinomial.
2((-4 + -1x)(3 + -2x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4

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 = {-4, 1.5}

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