4x(x-5)+7x=4x-4

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Solution for 4x(x-5)+7x=4x-4 equation: 


Simplifying
4x(x + -5) + 7x = 4x + -4

Reorder the terms:
4x(-5 + x) + 7x = 4x + -4
(-5 * 4x + x * 4x) + 7x = 4x + -4
(-20x + 4x2) + 7x = 4x + -4

Reorder the terms:
-20x + 7x + 4x2 = 4x + -4

Combine like terms: -20x + 7x = -13x
-13x + 4x2 = 4x + -4

Reorder the terms:
-13x + 4x2 = -4 + 4x

Solving
-13x + 4x2 = -4 + 4x

Solving for variable 'x'.

Reorder the terms:
4 + -13x + -4x + 4x2 = -4 + 4x + 4 + -4x

Combine like terms: -13x + -4x = -17x
4 + -17x + 4x2 = -4 + 4x + 4 + -4x

Reorder the terms:
4 + -17x + 4x2 = -4 + 4 + 4x + -4x

Combine like terms: -4 + 4 = 0
4 + -17x + 4x2 = 0 + 4x + -4x
4 + -17x + 4x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
4 + -17x + 4x2 = 0

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


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

Simplifying
1 + -4x = 0

Solving
1 + -4x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4x = 0 + -1
-4x = 0 + -1

Combine like terms: 0 + -1 = -1
-4x = -1

Divide each side by '-4'.
x = 0.25

Simplifying
x = 0.25

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {0.25, 4}

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