x(4x-6)-9=-3(-5x+3)+4x

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Solution for x(4x-6)-9=-3(-5x+3)+4x equation: 


Simplifying
x(4x + -6) + -9 = -3(-5x + 3) + 4x

Reorder the terms:
x(-6 + 4x) + -9 = -3(-5x + 3) + 4x
(-6 * x + 4x * x) + -9 = -3(-5x + 3) + 4x
(-6x + 4x2) + -9 = -3(-5x + 3) + 4x

Reorder the terms:
-9 + -6x + 4x2 = -3(-5x + 3) + 4x

Reorder the terms:
-9 + -6x + 4x2 = -3(3 + -5x) + 4x
-9 + -6x + 4x2 = (3 * -3 + -5x * -3) + 4x
-9 + -6x + 4x2 = (-9 + 15x) + 4x

Combine like terms: 15x + 4x = 19x
-9 + -6x + 4x2 = -9 + 19x

Add '9' to each side of the equation.
-9 + -6x + 9 + 4x2 = -9 + 9 + 19x

Reorder the terms:
-9 + 9 + -6x + 4x2 = -9 + 9 + 19x

Combine like terms: -9 + 9 = 0
0 + -6x + 4x2 = -9 + 9 + 19x
-6x + 4x2 = -9 + 9 + 19x

Combine like terms: -9 + 9 = 0
-6x + 4x2 = 0 + 19x
-6x + 4x2 = 19x

Solving
-6x + 4x2 = 19x

Solving for variable 'x'.

Reorder the terms:
-6x + -19x + 4x2 = 19x + -19x

Combine like terms: -6x + -19x = -25x
-25x + 4x2 = 19x + -19x

Combine like terms: 19x + -19x = 0
-25x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-25 + 4x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-25 + 4x)' equal to zero and attempt to solve:

Simplifying
-25 + 4x = 0

Solving
-25 + 4x = 0

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

Add '25' to each side of the equation.
-25 + 25 + 4x = 0 + 25

Combine like terms: -25 + 25 = 0
0 + 4x = 0 + 25
4x = 0 + 25

Combine like terms: 0 + 25 = 25
4x = 25

Divide each side by '4'.
x = 6.25

Simplifying
x = 6.25
Solution
x = {0, 6.25}

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