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

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


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

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

Reorder the terms:
-8x + 4x2 + 3(-3 + x) = -3
-8x + 4x2 + (-3 * 3 + x * 3) = -3
-8x + 4x2 + (-9 + 3x) = -3

Reorder the terms:
-9 + -8x + 3x + 4x2 = -3

Combine like terms: -8x + 3x = -5x
-9 + -5x + 4x2 = -3

Solving
-9 + -5x + 4x2 = -3

Solving for variable 'x'.

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

Combine like terms: -9 + 3 = -6
-6 + -5x + 4x2 = -3 + 3

Combine like terms: -3 + 3 = 0
-6 + -5x + 4x2 = 0

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


Subproblem 1
Set the factor '(-3 + -4x)' equal to zero and attempt to solve:

Simplifying
-3 + -4x = 0

Solving
-3 + -4x = 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 + -4x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -4x = 0 + 3
-4x = 0 + 3

Combine like terms: 0 + 3 = 3
-4x = 3

Divide each side by '-4'.
x = -0.75

Simplifying
x = -0.75

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-0.75, 2}

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