(5X+2)(3X-4)=15(X+1)(X+1)-13X

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Solution for (5X+2)(3X-4)=15(X+1)(X+1)-13X equation: 


Simplifying
(5X + 2)(3X + -4) = 15(X + 1)(X + 1) + -13X

Reorder the terms:
(2 + 5X)(3X + -4) = 15(X + 1)(X + 1) + -13X

Reorder the terms:
(2 + 5X)(-4 + 3X) = 15(X + 1)(X + 1) + -13X

Multiply (2 + 5X) * (-4 + 3X)
(2(-4 + 3X) + 5X * (-4 + 3X)) = 15(X + 1)(X + 1) + -13X
((-4 * 2 + 3X * 2) + 5X * (-4 + 3X)) = 15(X + 1)(X + 1) + -13X
((-8 + 6X) + 5X * (-4 + 3X)) = 15(X + 1)(X + 1) + -13X
(-8 + 6X + (-4 * 5X + 3X * 5X)) = 15(X + 1)(X + 1) + -13X
(-8 + 6X + (-20X + 15X2)) = 15(X + 1)(X + 1) + -13X

Combine like terms: 6X + -20X = -14X
(-8 + -14X + 15X2) = 15(X + 1)(X + 1) + -13X

Reorder the terms:
-8 + -14X + 15X2 = 15(1 + X)(X + 1) + -13X

Reorder the terms:
-8 + -14X + 15X2 = 15(1 + X)(1 + X) + -13X

Multiply (1 + X) * (1 + X)
-8 + -14X + 15X2 = 15(1(1 + X) + X(1 + X)) + -13X
-8 + -14X + 15X2 = 15((1 * 1 + X * 1) + X(1 + X)) + -13X
-8 + -14X + 15X2 = 15((1 + 1X) + X(1 + X)) + -13X
-8 + -14X + 15X2 = 15(1 + 1X + (1 * X + X * X)) + -13X
-8 + -14X + 15X2 = 15(1 + 1X + (1X + X2)) + -13X

Combine like terms: 1X + 1X = 2X
-8 + -14X + 15X2 = 15(1 + 2X + X2) + -13X
-8 + -14X + 15X2 = (1 * 15 + 2X * 15 + X2 * 15) + -13X
-8 + -14X + 15X2 = (15 + 30X + 15X2) + -13X

Reorder the terms:
-8 + -14X + 15X2 = 15 + 30X + -13X + 15X2

Combine like terms: 30X + -13X = 17X
-8 + -14X + 15X2 = 15 + 17X + 15X2

Add '-15X2' to each side of the equation.
-8 + -14X + 15X2 + -15X2 = 15 + 17X + 15X2 + -15X2

Combine like terms: 15X2 + -15X2 = 0
-8 + -14X + 0 = 15 + 17X + 15X2 + -15X2
-8 + -14X = 15 + 17X + 15X2 + -15X2

Combine like terms: 15X2 + -15X2 = 0
-8 + -14X = 15 + 17X + 0
-8 + -14X = 15 + 17X

Solving
-8 + -14X = 15 + 17X

Solving for variable 'X'.

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

Add '-17X' to each side of the equation.
-8 + -14X + -17X = 15 + 17X + -17X

Combine like terms: -14X + -17X = -31X
-8 + -31X = 15 + 17X + -17X

Combine like terms: 17X + -17X = 0
-8 + -31X = 15 + 0
-8 + -31X = 15

Add '8' to each side of the equation.
-8 + 8 + -31X = 15 + 8

Combine like terms: -8 + 8 = 0
0 + -31X = 15 + 8
-31X = 15 + 8

Combine like terms: 15 + 8 = 23
-31X = 23

Divide each side by '-31'.
X = -0.7419354839

Simplifying
X = -0.7419354839

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