4X^2-5X+15=7X+10

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Solution for 4X^2-5X+15=7X+10 equation: 


Simplifying
4X2 + -5X + 15 = 7X + 10

Reorder the terms:
15 + -5X + 4X2 = 7X + 10

Reorder the terms:
15 + -5X + 4X2 = 10 + 7X

Solving
15 + -5X + 4X2 = 10 + 7X

Solving for variable 'X'.

Reorder the terms:
15 + -10 + -5X + -7X + 4X2 = 10 + 7X + -10 + -7X

Combine like terms: 15 + -10 = 5
5 + -5X + -7X + 4X2 = 10 + 7X + -10 + -7X

Combine like terms: -5X + -7X = -12X
5 + -12X + 4X2 = 10 + 7X + -10 + -7X

Reorder the terms:
5 + -12X + 4X2 = 10 + -10 + 7X + -7X

Combine like terms: 10 + -10 = 0
5 + -12X + 4X2 = 0 + 7X + -7X
5 + -12X + 4X2 = 7X + -7X

Combine like terms: 7X + -7X = 0
5 + -12X + 4X2 = 0

Factor a trinomial.
(1 + -2X)(5 + -2X) = 0


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

Simplifying
1 + -2X = 0

Solving
1 + -2X = 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 + -2X = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2X = 0 + -1
-2X = 0 + -1

Combine like terms: 0 + -1 = -1
-2X = -1

Divide each side by '-2'.
X = 0.5

Simplifying
X = 0.5

Subproblem 2
Set the factor '(5 + -2X)' equal to zero and attempt to solve:

Simplifying
5 + -2X = 0

Solving
5 + -2X = 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 + -2X = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2X = 0 + -5
-2X = 0 + -5

Combine like terms: 0 + -5 = -5
-2X = -5

Divide each side by '-2'.
X = 2.5

Simplifying
X = 2.5
Solution
X = {0.5, 2.5}

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