4x^2-5x+10=7x+1

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Solution for 4x^2-5x+10=7x+1 equation: 


Simplifying
4x2 + -5x + 10 = 7x + 1

Reorder the terms:
10 + -5x + 4x2 = 7x + 1

Reorder the terms:
10 + -5x + 4x2 = 1 + 7x

Solving
10 + -5x + 4x2 = 1 + 7x

Solving for variable 'x'.

Reorder the terms:
10 + -1 + -5x + -7x + 4x2 = 1 + 7x + -1 + -7x

Combine like terms: 10 + -1 = 9
9 + -5x + -7x + 4x2 = 1 + 7x + -1 + -7x

Combine like terms: -5x + -7x = -12x
9 + -12x + 4x2 = 1 + 7x + -1 + -7x

Reorder the terms:
9 + -12x + 4x2 = 1 + -1 + 7x + -7x

Combine like terms: 1 + -1 = 0
9 + -12x + 4x2 = 0 + 7x + -7x
9 + -12x + 4x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
9 + -12x + 4x2 = 0

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


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

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5

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

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {1.5, 1.5}

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