(2-x)*(4x+5)=(2-x)*4+7-2x

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Solution for (2-x)*(4x+5)=(2-x)*4+7-2x equation: 


Simplifying
(2 + -1x)(4x + 5) = (2 + -1x) * 4 + 7 + -2x

Reorder the terms:
(2 + -1x)(5 + 4x) = (2 + -1x) * 4 + 7 + -2x

Multiply (2 + -1x) * (5 + 4x)
(2(5 + 4x) + -1x * (5 + 4x)) = (2 + -1x) * 4 + 7 + -2x
((5 * 2 + 4x * 2) + -1x * (5 + 4x)) = (2 + -1x) * 4 + 7 + -2x
((10 + 8x) + -1x * (5 + 4x)) = (2 + -1x) * 4 + 7 + -2x
(10 + 8x + (5 * -1x + 4x * -1x)) = (2 + -1x) * 4 + 7 + -2x
(10 + 8x + (-5x + -4x2)) = (2 + -1x) * 4 + 7 + -2x

Combine like terms: 8x + -5x = 3x
(10 + 3x + -4x2) = (2 + -1x) * 4 + 7 + -2x

Reorder the terms for easier multiplication:
10 + 3x + -4x2 = 4(2 + -1x) + 7 + -2x
10 + 3x + -4x2 = (2 * 4 + -1x * 4) + 7 + -2x
10 + 3x + -4x2 = (8 + -4x) + 7 + -2x

Reorder the terms:
10 + 3x + -4x2 = 8 + 7 + -4x + -2x

Combine like terms: 8 + 7 = 15
10 + 3x + -4x2 = 15 + -4x + -2x

Combine like terms: -4x + -2x = -6x
10 + 3x + -4x2 = 15 + -6x

Solving
10 + 3x + -4x2 = 15 + -6x

Solving for variable 'x'.

Reorder the terms:
10 + -15 + 3x + 6x + -4x2 = 15 + -6x + -15 + 6x

Combine like terms: 10 + -15 = -5
-5 + 3x + 6x + -4x2 = 15 + -6x + -15 + 6x

Combine like terms: 3x + 6x = 9x
-5 + 9x + -4x2 = 15 + -6x + -15 + 6x

Reorder the terms:
-5 + 9x + -4x2 = 15 + -15 + -6x + 6x

Combine like terms: 15 + -15 = 0
-5 + 9x + -4x2 = 0 + -6x + 6x
-5 + 9x + -4x2 = -6x + 6x

Combine like terms: -6x + 6x = 0
-5 + 9x + -4x2 = 0

Factor a trinomial.
(-5 + 4x)(1 + -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 '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
Solution
x = {1.25, 1}

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