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

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


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

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

Reorder the terms:
4x + 3x2 = 5(-9 + 2x)
4x + 3x2 = (-9 * 5 + 2x * 5)
4x + 3x2 = (-45 + 10x)

Solving
4x + 3x2 = -45 + 10x

Solving for variable 'x'.

Reorder the terms:
45 + 4x + -10x + 3x2 = -45 + 10x + 45 + -10x

Combine like terms: 4x + -10x = -6x
45 + -6x + 3x2 = -45 + 10x + 45 + -10x

Reorder the terms:
45 + -6x + 3x2 = -45 + 45 + 10x + -10x

Combine like terms: -45 + 45 = 0
45 + -6x + 3x2 = 0 + 10x + -10x
45 + -6x + 3x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
45 + -6x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(15 + -2x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(15 + -2x + x2)' equal to zero and attempt to solve:

Simplifying
15 + -2x + x2 = 0

Solving
15 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + -2x + -15 + x2 = 0 + -15

Reorder the terms:
15 + -15 + -2x + x2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -2x + x2 = 0 + -15
-2x + x2 = 0 + -15

Combine like terms: 0 + -15 = -15
-2x + x2 = -15

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = -15 + 1

Reorder the terms:
1 + -2x + x2 = -15 + 1

Combine like terms: -15 + 1 = -14
1 + -2x + x2 = -14

Factor a perfect square on the left side:
(x + -1)(x + -1) = -14

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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