x(3x-5)+x(4x-3)=(7x+4)(x-4)

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Solution for x(3x-5)+x(4x-3)=(7x+4)(x-4) equation: 


Simplifying
x(3x + -5) + x(4x + -3) = (7x + 4)(x + -4)

Reorder the terms:
x(-5 + 3x) + x(4x + -3) = (7x + 4)(x + -4)
(-5 * x + 3x * x) + x(4x + -3) = (7x + 4)(x + -4)
(-5x + 3x2) + x(4x + -3) = (7x + 4)(x + -4)

Reorder the terms:
-5x + 3x2 + x(-3 + 4x) = (7x + 4)(x + -4)
-5x + 3x2 + (-3 * x + 4x * x) = (7x + 4)(x + -4)
-5x + 3x2 + (-3x + 4x2) = (7x + 4)(x + -4)

Reorder the terms:
-5x + -3x + 3x2 + 4x2 = (7x + 4)(x + -4)

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

Combine like terms: 3x2 + 4x2 = 7x2
-8x + 7x2 = (7x + 4)(x + -4)

Reorder the terms:
-8x + 7x2 = (4 + 7x)(x + -4)

Reorder the terms:
-8x + 7x2 = (4 + 7x)(-4 + x)

Multiply (4 + 7x) * (-4 + x)
-8x + 7x2 = (4(-4 + x) + 7x * (-4 + x))
-8x + 7x2 = ((-4 * 4 + x * 4) + 7x * (-4 + x))
-8x + 7x2 = ((-16 + 4x) + 7x * (-4 + x))
-8x + 7x2 = (-16 + 4x + (-4 * 7x + x * 7x))
-8x + 7x2 = (-16 + 4x + (-28x + 7x2))

Combine like terms: 4x + -28x = -24x
-8x + 7x2 = (-16 + -24x + 7x2)

Add '-7x2' to each side of the equation.
-8x + 7x2 + -7x2 = -16 + -24x + 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
-8x + 0 = -16 + -24x + 7x2 + -7x2
-8x = -16 + -24x + 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
-8x = -16 + -24x + 0
-8x = -16 + -24x

Solving
-8x = -16 + -24x

Solving for variable 'x'.

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

Add '24x' to each side of the equation.
-8x + 24x = -16 + -24x + 24x

Combine like terms: -8x + 24x = 16x
16x = -16 + -24x + 24x

Combine like terms: -24x + 24x = 0
16x = -16 + 0
16x = -16

Divide each side by '16'.
x = -1

Simplifying
x = -1

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