4x(x-3)+5(x-3)=0

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Solution for 4x(x-3)+5(x-3)=0 equation: 


Simplifying
4x(x + -3) + 5(x + -3) = 0

Reorder the terms:
4x(-3 + x) + 5(x + -3) = 0
(-3 * 4x + x * 4x) + 5(x + -3) = 0
(-12x + 4x2) + 5(x + -3) = 0

Reorder the terms:
-12x + 4x2 + 5(-3 + x) = 0
-12x + 4x2 + (-3 * 5 + x * 5) = 0
-12x + 4x2 + (-15 + 5x) = 0

Reorder the terms:
-15 + -12x + 5x + 4x2 = 0

Combine like terms: -12x + 5x = -7x
-15 + -7x + 4x2 = 0

Solving
-15 + -7x + 4x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-5 + -4x)(3 + -1x) = 0


Subproblem 1
Set the factor '(-5 + -4x)' equal to zero and attempt to solve:

Simplifying
-5 + -4x = 0

Solving
-5 + -4x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -4x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -4x = 0 + 5
-4x = 0 + 5

Combine like terms: 0 + 5 = 5
-4x = 5

Divide each side by '-4'.
x = -1.25

Simplifying
x = -1.25

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-1.25, 3}

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