(x-10)(4x-3)=0

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Solution for (x-10)(4x-3)=0 equation: 


Simplifying
(x + -10)(4x + -3) = 0

Reorder the terms:
(-10 + x)(4x + -3) = 0

Reorder the terms:
(-10 + x)(-3 + 4x) = 0

Multiply (-10 + x) * (-3 + 4x)
(-10(-3 + 4x) + x(-3 + 4x)) = 0
((-3 * -10 + 4x * -10) + x(-3 + 4x)) = 0
((30 + -40x) + x(-3 + 4x)) = 0
(30 + -40x + (-3 * x + 4x * x)) = 0
(30 + -40x + (-3x + 4x2)) = 0

Combine like terms: -40x + -3x = -43x
(30 + -43x + 4x2) = 0

Solving
30 + -43x + 4x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3 + -4x)(10 + -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 '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {0.75, 10}

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